fix(web): respect Vite base in dev API proxy

[voidzero]

Summary

Follow-up to #110, addressing the optional dev middleware issue raised by @offendingcommit during review. Thanks for reviewing and merging the original PR!

• Mount the Vite dev API proxy using the resolved server.config.base, so a dev server started with --base /honcho/ forwards /honcho/api/* correctly.
• Add an HTTP regression check for / and /honcho/, verifying that the upstream receives the correct path and query string.
• Run the regression check as part of the existing web test command.

Testing

• Before the fix, the / case passed and the /honcho/ case failed: the request returned the SPA HTML instead of the upstream response.
• After the fix, both HTTP regression cases passed.
• make ci-web passed with all tasks executed: lint, typecheck, 116 existing tests, two proxy regression tests, and production build.
• Biome checks on all three changed files and git diff --check passed.