feat: add biome, fix format and lint

[hauserkristof]

This PR adds biome to the web codebase, fixes lint and formatting errors.

This is related to #13 making it easier to review.

[hauserkristof]

hey @theacodes can you take a look at this (and all later PRs) please?

[theacodes]

Sure. For this one there's two things:

1. I think it might be out of date? There seems to be unrelated commits.
2. What's the purpose of adding biome? Is it just for formatting? (I actually thought this repo was using prettier but it seems when I hacked this together I didn't bother, lol)

[hauserkristof]

• well, nope, this is up to date.
• we have talked about biome in Feature/mirror back layers #13

we also talked in #13 to separate some things, so here is this PR, and #20 and #21 also

[theacodes]

Oh man my apologies, I'm so forgetful lol. In that case, this looks good then.