I was just watching this LTT video showcasing conductive pen repair:
https://www.youtube.com/watch?v=WY3d8N21OAE

And aside from just considering that vs solder patches, there's a point I want to touch on that I'm not sure how many folks already know.

It isn't going to be acid corrosion from leaky batteries (rechargeable or otherwise) unless you've got a lead-acid rechargeable battery that's leaked onto things, which is going to be rare out side of UPS repair and some autometive/industrial stuff ... and maybe some old notebooks/portables.

Almost verything else is going to be basic (alkaline) electrolyte based (usually potassium hydroxide, sometimes sodium) for typical zinc-carbon alkaline batteries, NiCD, NiMH, and most types of Lithium batteries.
(though the 1.5V iron sulfide ones, ie lithium AA batteries, are a bit weird and have hydrogen sulfide or lithium sulfide leakage to consider aside from the quite dry paste electrolyte, also extremely unlikely to leak unless physically punctured)

The remainder of almost all common consumer/commercial small cell batteries are going to have some type of salt as the electrolyte: cheap, old fashioned zinc carbon dry cells use ammonium chloride, a slightly beefier variant uses zinc chloride (and is usually labeled such or 'super heavy duty' ). Both of those are slightly acidic in solution, but not acids themselves, and zinc chloride (also present in degraded ammonium chloride dry cells) will react with baking soda to make it bubble: turns into Zinc carbonate, sodium chloride, and CO2.

Copper is sensitive to ammonium salts and ammonia (it dissolves the oxide coating and accelerates corrosion) and zinc chloride itself is fairly corrosive and extremely hygroscopic (absorbs humidity, in this case to the point of turning to liquid). Ammonium chloride is hygroscopic but not as bad as zinc chloride.

Potassium hydroxide is extremely hygroscopic as well (also typically turning to liquid in open air outside of very dry climates) can react with copper's oxide layer too (forming copper-potassium salts that eventually turn into copper carbonate and potassium bicarbonate with long enough exposure to air) Copper carbonate is pretty harmless, but potassium bicarbonate is hygroscopic enough to at least encourage some corrosion from dampness, albeit not reactive or caustic like the hydroxide. (potassium hydroxide is also nasty to get on skin, at least in significant amounts, especially if hot: it turns the fatty portions of skin cells into soap, and eats away at it ... though for tiny bits of battery corrosion, I'd be mostly careful of eye/nose/mucus membrane contact)

Potassium hydroxide also seems to eat into the resin PCBs are made of and diffuse into it, causing bubbling of corrosion under the surface and trapping corrosive material inside. And aside from breaking traces, it could bridge traces with conductive, damp corrosion-salt bubbles. (in this case, I'd probably recommend scraping open the affected PCB area and cleaning off most of the contamination, potentially with just water-dampened paper/cloth/swab but see below)

Some rechargeable cells might actually use some other salt electrolytes, maybe organic salts (acetate, citrate, etc) and I think some rechargeable lithium cells use that and maybe some types of Nickel based ones, but alkaline based NiCD and NiMH seem to account for the vast majority (old and new).

I've seen some users suggesting (or at least recounting) use of vinegar for cleaning corrosion, but I'd tend to avoid that unless it's very heavily rinsed afterward as copper, potassium, sodium, and zinc acetate are all quite hygroscopic and promote corrosion. Distilled water would be good for a lot of situations, as would diluted (or cheap 50%) rubbing alcohol as both should dissolve the highly soluble corrosion/electrolyte components well, and if you're not going to solder onto the surfaces, it should be fine to leave the insoluble copper oxide/carbonate patina alone or stabilize it with something water resistant (maybe some solvent based glue or lacquer ... clear nail polish, or just vaseline: obviously mind damaging silkscreened markings, insulation, and such that might smear from solvent exposure).

Tap water might be OK too, but if you don't know the specific contaminants in your water I'd avoid it. (around here, it's very low to no chlorine added, but very hard: tons of calcium bicarbonate dissolved and probably some magnesium, so it will leave some calcium carbonate residue, which is mostly harmless, but could also leave calcium chloride behind if zinc chloride or ammonium chloride is present: no good, but enough rinsing would do away with that too and is not relevant for alkaline corrosion)

Hard water can also react with the potassium hydroxide to form calcium hydroxide (almost insoluble) and potassium bicarbonate, but this is mostly a non-issue as well. (the calcium hydroxide scum will quickly turn into calcium carbonate anyway, so pretty much the same difference)

Softened water or heavily chlorinated water would be more problematic due to higher sodium and/or chlorine and chloride content. (more corrosive residue)

However, for actually neutralizing/stabilizing corroded areas and residue with minimal abbrasion/scraping, I think carbonated water would be a really safe bet. That would turn any of the remaining alkaline electrolyte into bicarbonate while also flushing most of it away just as well as distilled water.

A small amount of baking soda (sodium bicarbonate) may also be useful for cleaning some of the crust/corrosion off, especially for solder prep (very mild abbrasion, potentially enough to not need any acid for further cleaning and just rosin and solder for tinning). If it's just alkaline leakage present, the bicarbonate shouldn't react to form anything worse than what's there (potassium hydroxide will react to form potassium carbonate and sodium carbonate, both of which will turn into more bicarbonate with enough exposure to air) and any baking soda residue will be relatively harmless. (it's one of the least soluble sodium salts, minimally hygroscopic and relatively non-corrosive)

And while not relevant to most (or any?) PCB material, alkali/bases tend to be highly corrosive to aluminum components, dissolving the protective oxide layer (and even thick, hard anodized coatings) and causing both water and air to react fairly rapidly. (forming aluminum hydroxide, hydrogen gas, and aluminum oxide) Aluminum on-copper or steel contacts would further accelerate corrosion from battery action. (electrochemical cell action)

The aluminum issue would be much more common inside some flashlights, disposable battery operated electronics (radios, game consoles, toys, etc), and the like. That's also the place you'll likely run into steel or plated-steel corrosion a lot (coil or leaf/V spring contacts in battery holders) as well as likely have crystalized caustic potassium hydroxide left over. (unless well ventilated, it's probably not going to turn into carbonate)

Worst-case for me was a rather nice, waterproof flashlight that had alkaline cells leak inside and corrode for a long while, with all the water sealed in. (ate into the machined aluminum reflector/bulb holder module)
Cheap-ass dry-cells or expensive lithium AAs wouldn't have done that ...

There's also some possible concern for corroded solder and tinning. On top of corrosive lead and tin salts that might result, soluble lead salts (especially acetate) would be among the more toxic and easily absorbed forms of lead, and lead carbonate (a likely result of alkaline corrosion on leaded solder) will quickly dissolve in vinegar to form acetate (lead oxide will, too, and lead metal will slowly dissolve). So more reason to be extra cautious of using vinegar (acetic acid) and a few other organic acids, like the citric acid in lemon juice.

Lead acetate can be easily absorbed by skin, but is more dangerous if ingested, and tastes sweet. (it's also called: sugar of lead)

The carbonated water method should keep lead in its insoluble carbonate or oxide form, and the baking soda treatment should also react with almost any soluble lead salt to form carbonate + a sodium salt. So another added safety perk there.

Beyond that I guess there's the modest concern of corrosion from left-over rosin (usually minor and sometimes even protective against alkaline corrosion) and the broader topic of corrosion caused by humid/damp storage or being left outside for extended periods (or leaky sheds, garages, etc) or contaminated by animals. (rodent or bat infestations in attic/garage/shed) Maybe insect damage or contaimation, too.

And if anyone else has experience with cleaning and repairing corrosion or any tips or tricks, please add them.