I primarily use my camera for wildlife photography

This would alone be a reason to switch. Generally bridge cameras don't have as marvelously perfect autofocus as DSLRs / mirrorless camera. However, wildlife photography isn't the most budget-friendly hobby. Ideally you'd have a good coverage of autofocus points and rapid burst shot rate, which won't be found in the cheapest DSLRs.

What I'm confused about, are the actual trade offs between a DSLR, and a bridge.

DSLR / mirrorless generally has much, much better autofocus, whereas cheaper cameras often hunt for focus so long that you miss shots unless the animals you shoot are very static.

Also the lenses have better optical quality, zoom is faster since it happens by rotating the lens barrel not by a motor.

However, DSLRs are generally accepted to be better quality anyway (especially full frame ones)

Not for wildlife (full frame I mean). For wildlife, generally you prefer crop cameras although Canon has managed to make a full frame 800mm f/11 lens that might make full frame cameras acceptable for medium-budget wildlife photography if you have the funds for mirrorless. But at least with DLSRs (not mirrorless), you want crop, since lenses are usually f/5.6 or f/6.3 at the very least for autofocus to work, and 400mm f/5.6 gives so much better reach with crop cameras than it does with full frame cameras. Generally for wildlife, crop cameras are preferable. On the very high end, there are full frame cameras with such huge megapixel count that pixel density equals that of crop cameras, but you don't use those usually for wildlife, since huge megapixel count means shooting speed in burst isn't fast anymore.

Zoom: most lenses, even really long ones, seem to have very small zoom as opposed to my Canon. I'm not sure whether this is really bad, because I have seen, especially with full-frames, that its easy to crop images without losing quality for DSLRs.

The key here is that you select the lens for the usage. For example 55-250mm lens on a crop camera is 88-400mm full frame equivalent. Would it be better to have 25-400mm 16x zoom? No, because a 25-400mm lens is heavier, more expensive, has smaller aperture and worse optical quality than a lens built to be a real tele lens. Lenses aren't jacks of all trades. You select a lens for the usage. So-called superzooms are available too but then you limit your reach at the tele end, have to pay a lot of money for them, have to carry lot of weight for you, have to accept small aperture and poor optical quality. Usually those who use DLSRs / mirrorless cameras don't want them, but maybe if you're on a vacation, traveling light, and don't want to change lenses, you might prefer one.

AF points: again, due to budget reasons, I'll probably have an average of 11 points if I get a new DSLR. I think on my Canon it's 7. So notably an improvement, but still not the best for wildlife photography.

This is what you want to focus on (pun intended). Also, you want to buy a camera with "lens drive when AF impossible" option in the menu. I would recommend a used Canon 70D for example. It has reasonable burst rate, good autofocus and the "lens drive when AF impossible" option allowing you to stop hunting for focus when it doesn't help. Also, it's a crop camera which means a 400mm prime makes a marvelously long reach lens for example. You can buy a Canon 70D for ~300-400 EUR used where I live (adjust for currency and tax rates for other areas), but that obviously doesn't come with a lens. Add another ~350 EUR and you get yourself a new 55-250mm lens, or ~150 EUR for a used 55-250mm IS II which I would avoid due to its older focus motor technology.

However, wildlife photography is a neverending money pit. Once you get the 70D and 55-250, you will start lusting after a 400mm f/5.6 which is only available used as the new ones have been discontinued. Some time ago, you would expect to pay over 1000EUR for a used quality one, but today many photographers are moving to EOS R mirrorless, meaning quality EF glass can be bought used for good prices, maybe even as cheaply as 650EUR if you can find a good deal.