[WRONG BRANCH] fix(providers): allow same-origin connection tests

[luvs01]

Motivation

• The connection-test UI and handler treated an empty apiBase as absent, which hid the Test connection control for the default same-origin GUI deployment even though fetch(${apiBase}/api/...) with apiBase === "" should resolve to /api/... and work.

Description

• Relax the early-exit and rendering checks to distinguish a missing apiBase from an intentionally empty same-origin base by checking apiBase === undefined and apiBase !== undefined respectively in gui/src/components/provider-workspace/ProviderOverview.tsx.
• Keep the existing fetch URL construction ( ${apiBase}/api/providers/test?name=... ) so an empty apiBase produces the same-origin /api/providers/test?... request.
• Add a focused regression test connection test supports the default same-origin API base to gui/tests/provider-overview-notes-save.test.tsx that verifies the button renders with apiBase = "", the same-origin request is issued, and a successful result is displayed.

Testing

• Ran the targeted tests with cd gui && bun test tests/provider-overview-notes-save.test.tsx, and the file's tests (including the new case) passed (6 pass, 0 fail).
• Ran cd gui && bun run lint and cd gui && bun run build, and both completed successfully (Vite build emitted only existing chunk-size warnings).
• Ran the broader GUI test run cd gui && bun test tests; the targeted regression passed but the full suite reported unrelated failures in other tests and one environment incompatibility under the local Bun version, which are not caused by this focused change.

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📥 Commits

Reviewing files that changed from the base of the PR and between 57140d6 and 05e4640.

📒 Files selected for processing (2)

• gui/src/components/provider-workspace/ProviderOverview.tsx
• gui/tests/provider-overview-notes-save.test.tsx

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[github-actions]

✅ Deterministic PR hygiene checks passed.

[github-actions]

⏳ DRAFT

• wrong target branch (main); retarget to dev. UI screenshot required.

What to do

• Retarget this PR to dev — all contributions go to dev.
• Add a screenshot of the UI change to the PR description.

Its title has been prefixed with [WRONG BRANCH].
This pull request was already a draft. Its draft status will be preserved after every issue above is resolved.