Add browser-level end-to-end test coverage

## Problem

The repo has strong unit and component coverage (170+ unit and 25 component test files) but no browser-level end-to-end tests. Nothing exercises the real stack: the UI driving real queries through the proxy server against a real graph database.

Two recent bugs illustrate the gap:

- #2068: unit tests passed while the rendered UI sent an unlimited expansion request. Only a browser-level test observing the outgoing query catches this class of bug.
- #1977: error display behavior depended on how a real server response flows through fetch, parsing, and the error boundary. Reproducing it required a live browser against a live endpoint.

## Proposal

A small Playwright suite that runs the full stack locally and in CI:

1. `tinkerpop/gremlin-server` in Docker using the bundled `conf/gremlin-server-rest-modern.yaml` (HTTP endpoint, modern sample graph preloaded, no auth). Starts in seconds and needs no AWS resources.
2. The existing proxy server and dev server, exactly as `pnpm dev` runs them.
3. Playwright driving Chrome: create a connection, sync schema, search, add nodes, expand neighbors, and assert on both the rendered UI and the captured Gremlin requests.

I have a working prototype of this exact stack. It produced the before/after evidence on #2069 (screenshots plus captured request bodies proving the missing `.range()` clause) and an earlier variant produced the evidence on #1979 with a stub server. The pieces that exist today: launch orchestration, connection setup flow, schema sync wait, node-to-canvas flow, expand panel interaction, and network capture.

## Suggested starting scope

- One smoke test per query language reachable with local engines (Gremlin now via TinkerPop; openCypher and SPARQL as follow-ups if suitable local engines are agreed on)
- The critical analyst path: connect, sync, search, add to canvas, expand with limit
- CI job with the Docker service, gated to run on PRs

## Out of scope for a first pass

- Visual regression testing
- Neptune-specific behavior (engine differences like #1798 still need a real cluster)
- Full cross-browser matrix

Happy to contribute this incrementally, starting with the harness plus two or three smoke tests, if the approach sounds right to the team.

Start with the existing `pnpm dev` entry point and the bundled `conf/gremlin-server-rest-modern.yaml` used by TinkerPop. Review the existing launch orchestration, connection setup, schema sync, canvas flow, expand interaction, and network capture from the working prototype. Done means a Playwright smoke path runs against the local Docker-backed stack, checks the UI and captured Gremlin requests, and is gated in CI.

Written by the indexing model from the issue text.