All I'm looking for is a way to get the card running in SVGA resolution on programs like AutoSketch and Windows, maybe some SVGA graphic adventures, too, if that's possible.
800x600 on most of these old cards was with 56Hz screen refresh rate, as Elianda correctly wrote.
1024x768 was commonly at 43Hz interlaced.
Not sure what LCDs do with these odd frequencies.
Edit: How about Realtek cards ? Just seen a few online, approx. from the same time period.
You are just experiencing what is normal for "super" vgas that have broken VGA compatibility, bad drivers and bad hardware.
Graphics cards are not wine... they do not become better when aging.
In the time between approx 1985 to 1995 I did much hardware service and support.
So I always give the advice to avoid Trident, Oak, Cirrus, Realtek, WD, UMC, or, in short, all these budget cards.
Even expensive cards with efficient hype marketing were often fundamentally flawed (explains why for example there are no happy retro DOS gaming users of Paradise and ATI cards).
Even back then it was very frustrating with those, as these shared the same things: bad drivers, hardware incompatibilities (no or distorted output with many games), incorrectly boasting performance and graphics modes that turn out to work poorly if at all.
Common with those are also bad (low-rated) DACs. Your Oak has a 35MHz one, this is outrageous, as you won't get a sharp picture at 800x600 anymore. For myself, I do not accept DACs below 80MHz. (hint: you can put a higher-rated one in to improve image quality. Good buffering of the supply voltage is necessary too, just add .47uf or so diagonally stretched between GND and Vcc)
Another possible reason is that the 36MHz crystal just got damaged (they are very sensitive). Well, if you look at that Oak cards' frequency generation, it is hard to find a worse/cheaper one.
If you want hassle-free DOS retro gaming and good Windows drivers on ISA bus, there is only Tseng and VideoSeven (i.e. Headland chips), and the late ISA early S3.
Sadly these cards make only about 10% of what is being offered on the popular auction house, and they are (justifiedly) commonly in the upper third of the price range.