Use biome for frontend formatting and linting

[isakstenstrom]

NOTE: This is a stacked PR. Please merge #226, #227, #228, #229, #230, #231, #232, #233, #234 first.

Setup Biome as formatter and linter for the frontend. This is done in 3 steps:

• One commit that configures biome and the CI checks
• One commit that fixes all lint errors in the application
• One commit that runs the auto formatting on the entire frontend.

How do use:

• Format everything: npm run format
• Lint everything: npm run lint
• Format, lint and sort imports: npm run check
• Do everything in CI: npm run biome-ci

Closes #75