Migrate proxy server routes to a consistent /api routing strategy

## Desired outcome

Graph Explorer's proxy server should expose its routes under a consistent, industry-standard **`/api/` prefix**, cleanly separated from the static client assets served at the root. Today the proxy routes (`/gremlin`, `/sparql`, `/openCypher`, `/summary`, `/status`, `/logger`, `/defaultConnection`, etc.) live at the root alongside the client, which is inconsistent with common practice and makes routing harder to reason about behind reverse proxies.

The end state: all server API endpoints live under `/api/*`, the client is served at `/`, and the old root-level routes are gone.

## Status

**Deferred.** This is a code-quality / consistency improvement, not required for any committed release. The related proxy-URL work (see related issue) was delivered by a different mechanism, so this routing migration is no longer blocking — but it remains desirable and is recorded here for a future release. The child tasks capture the concrete slices.

> [!IMPORTANT]
> Internal only — this issue is maintained by the core team and is not accepting external contributions.

Start by locating the proxy server route definitions for /gremlin, /sparql, /openCypher, /summary, /status, /logger, and /defaultConnection. Review how the client is served at the root, then verify that every API endpoint uses the /api/ prefix and that the old root-level routes are removed while static assets remain at /.

Written by the indexing model from the issue text.