feat: detect and log Dolt shared server mode

[jdillon]

Summary

• Parse shared_server field from bd dolt show --json output
• Include server mode (shared vs per-project) in connection log
• Store sharedServer on DoltConnectionInfo for future mode-aware behavior (e.g., suppressing stop in shared mode)

Test plan

• Open extension with a shared-server project, check Beads output channel shows (shared server)
• Open extension with a per-project server, check output shows (per-project server)

Summary by CodeRabbit

• Enhancements
  • Connection logs now display the server mode (shared or non-shared) when establishing Dolt SQL connections, providing clearer connection diagnostics.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: 5b784d4b-f56e-42d4-a36e-eba471807636

📥 Commits

Reviewing files that changed from the base of the PR and between 1eccde3 and 2bf9807.

📒 Files selected for processing (1)

• src/backend/BeadsDoltBackend.ts

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📝 Walkthrough

Walkthrough

The changes extend Dolt connection metadata handling by introducing a sharedServer field to track whether a Dolt server is shared. Connection logging now includes the server mode information, and connection info derivation incorporates this new field. No public APIs were modified.

Changes

Cohort / File(s)	Summary
Connection Metadata Extension src/backend/BeadsDoltBackend.ts	Added sharedServer: boolean field to connection metadata interfaces and updated connection logging to display server mode. Connection info derivation now includes sharedServer: showInfo.shared_server === true. Pool creation behavior unchanged.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~8 minutes

Poem

🐰 A shared server, now we know,
With metadata's helpful glow,
Connection logs now tell the tale,
Of shared or solo, without fail! 🔌

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title 'feat: detect and log Dolt shared server mode' accurately and concisely describes the main change: adding detection and logging of Dolt shared server mode based on the shared_server field.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

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✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch feat/shared-server-detection

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