First, I can recreate the problem on Firefox and Chrome. Unfortunately, I don't know what to do so that dominion.games uses the standard font size and every other website the larger font size
, but see my sugesttion at the end.
1) Yes. When I changed the font to "Large" in the Chrome settings, I get the same kind of problem that you showed. When I changed it back, it was OK again. I assume that will happen for you as well.
2) I don't think Mircrosoft allows different kinds of Edge on the same system, but I'm by no means an expert on this.
3) Yes, you can access that on that page and change the magnification of every website, but you can also change that per web page (as per CTRL-MouseWhelUp/Donw). Unfortunately, it doesn't solve the problem by itself: If you have the larger fonts enabled, then increasing the magnification just makes the unreadable card bigger, but the coin symbol is still above the text.
So from what I can see, the only solution right now would be to set the font size to normal while you are playing and change it back once you are done. Cumbersome, IMO, and if you want to read other websites while playing, they use normal font size.
One option to prevent that (which I use for myself with Firefox) is to create another profile in Chrome, by clicking on the little person icon in the top right:
That creates another profile, and all settings belong to a profile. So you can change the settings for this profile to work OK with dominion.games (setting font size to "middle", maybe increase magnification), but they don't affect your standard profile, that keeps whatever options you've chosen (like large fonts).
The "Add profile" dialog also creates a new shortcut on the desktop, which you can rename to "Dominion" and use it to start Dominion. It will create a new window, not a tab in your existing Chrome browser, but that's the only difference. This seems to me the most promising approach.