This looks fairly mild and definitely nowhere near to a point where repairs aren't gonna be worth it. That battery should be removed immediately, wiggle it until it comes off if you cannot desolder it.
Vinegar is used to neutralize the acid residues, isopropanol or other cleaning alcohol to clean up things. Rest is matter of fixing broken traces, vias and any damaged components (soldering required).

oh... this is typical varta destruction...
what you can do until someone with repair skills can patch it up:
- cut off the battery , use some pliers or something - just remove it completely
- soak the area with vinegar or lemon juice to neutralize the battery acid , use a toothbrush to get the fluid in all nooks and crannies
- after 10~15mins clean up the vinegar/lemonjuice with something like isopropyl alcohol (don;t wash with water when acid is active all you'll do is spread it further)
- once cleaned find someone to patch it

I think that covers it 😀

honestly from the pic it seems very possible that no traces or vias have yet been destroyed

if you remove the heinous battery ASAP and clean it up as described in the previous posts, you might just be good to go

Thanks for the advice everyone. Planning a Walmart trip this afternoon to pick up some things, will grab some vinegar and work on the Amiga today.

I agree with the above. Looks pretty good still. My worst patient was a Vtech Laser Turbo XT, had the battery on an expansion card. Leaked all over the cache sockets. At least they weren't populated.

I have seen so much worse, think you are pretty lucky but get it off asap

I appear to have gotten rid of the corrosion and the motherboard is looking pretty good (assuming my thumb-fingered wielding of the soldering iron didn't cause damage I didn't see).

I pulled the barrel battery... now I need to look for a replacement.

It's 3.6v NiCad, Varta brand, 3/V60R, 60mAh, 14h, 6mH

Could I replace it with a 3.6v CR2032 *rechargeable* button battery?
What must I look out for in a replacement battery?

(it also had 3 feet sticking into the motherboard, can't figure out why).

So I bought a replacement 2032 battery from Amigakit in the UK (only the 2nd package I can recall getting from the UK...)
After much trial and tribulation, I got it installed in my A3000... and... she works!
I haven't really tested to see if the battery is saving CMOS settings, but... did I mention that she works?
It appears that I can access both HDs, which surprised me. I am surprised.

The floppy drive is acting up, however... DF0 appears on screen as ??? and there's no reaction when I insert a disk.
I probably almost certainly have the cabling connected wrong.
In any event, I'll probably get a GoTek floppy emulator for it (does the bezel come off on those things? The A3000 has custom cutouts for floppies).

I are so happy that my baby is alive again!
Almost EIGHT YEARS sitting in the closet.
Not sure what I'm going to do with her, now.
I understand there are new accelerators and expansion boards, but of course they're expensive; that would mean rescheduling some of my other projects to shift the funds to support my A3000.
Gotta decide if that's worth it.

Anyway... Amiga saved from evil battery! Thanks for all the advice; that helped!