Migrate to Vitest Browser Mode

[kentcdodds]

The future is here and vitest browser mode is it. Let's remove JSDOM in favor of testing our browser code in a real browser. For Node-based tests, we can continue to use vitest as is. I just want to get rid of JSDOM.

@kettanaito, would you be at all interested in taking a look at this?

[kettanaito]

@kentcdodds, yes! I'd love to help out and see Browser Mode used in Epic Stack. Let me plan something for next week, I should have some time for this.