Thanks for playing, fren!
You have various options for skipping, you can press spacebar instead of clicking. You can click to a specific phase in the middle bar and the game skips until that phase. And then you can press 4 or select the fourth option on the right side to skip the turn. I know these things aren't super clear but the menu has a "how to play/controls" button that also tells you this information.
The AI has some checks not to play cards with costs that would kill it, but it seems to not be working in some cases, I'll look into that!