chore: remove Next.js and repoint CI at the SvelteKit layout

sync-data.yml now writes static/champions.json. This is the edit that had to
land with the deletion of public/: the workflow reports success regardless of
which path it writes, so a miss would have left the weekly sync green while
the live game 404'd on data load.

deploy.yml publishes build/ and passes BASE_PATH. Adds ci.yml, which runs
test, lint, and build on pull_request and pushes to main -- the repo had no
PR-triggered workflow before, so 'green before merge' was previously
unenforceable.

Deletes app/, components/, lib/, public/, next.config.mjs and
postcss.config.mjs, drops the Next and React dependencies, and swaps ESLint
onto eslint-plugin-svelte. sharp and unrs-resolver left pnpm's allowBuilds
because both arrived with Next and pnpm why now reports no dependents.

web/.github/workflows/deploy.yml

@@ -31,11 +31,11 @@ jobs:
 
       - run: pnpm build
         env:
-          NEXT_PUBLIC_BASE_PATH: /${{ github.event.repository.name }}
+          BASE_PATH: /${{ github.event.repository.name }}
 
       - uses: actions/upload-pages-artifact@v5
         with:
-          path: out
+          path: build
 
   deploy:
     needs: build