Update UI packages, upgrade to Vite 7 and Storybook 9

Updates to vulnerable packages have been applied. This also included updating Vite to 6. It was done in an initial merge request, which is now merged, so in case upgrading to Vite 7 (and Storybook 9, which we need in order to use Vite 7) takes longer, we're not holding up those updates.

My initial testing showed that with Vite 7 there are problems in dev mode when importing the WASM files for @swc/wasm-web and tailwindcss-in-browser. We've been using optimizeDeps.exclude for those, which previously worked.

balintbrews → changed the visibility of the branch 3537135-npm-audit-fix to hidden.

The backport tag probably only applies to the first MR that's already in.

Removing the "backport" tag since it doesn't apply to what's in the issue title and #7 already cherry picked the part that's not in the issue title.