Make searchable dropdown selections stable

[mbakgun]

Summary

• Replaced the new credential type picker with the shared searchable dropdown.
• Switched AI Agent, LLM, fallback model, and dashboard chat model pickers to searchable dropdowns.
• Fixed the searchable dropdown so clicking the already-selected option keeps the selection instead of clearing the displayed value.
• Updated credential E2E coverage for the searchable type picker and added a regression test for reselecting the current type.

Impact

Users can search long credential/model lists consistently, and the new credential dialog no longer loses the selected type when the current option is clicked again.

Validation

• bun run lint (passes; existing CodexFollowupView.vue vue/no-v-html warnings remain)
• bun run typecheck
• ./run_e2e.sh e2e/tab-credentials.spec.ts (9 passed)
• git diff --check
• SECRET_KEY=test-secret-key-for-tests-only-32-bytes ./check.sh ran; frontend/backend lint passed, but the full parallel backend suite reported timeout/flaky failures in test_chart_output_node.py and test_mcp_jsonrpc_tool_calls.py.
• SECRET_KEY=test-secret-key-for-tests-only-32-bytes uv run pytest tests/test_chart_output_node.py tests/test_mcp_jsonrpc_tool_calls.py -v (7 passed on rerun).