refactor(core): move FTS execution behind FtsBackend and bind the read path to scope

[phernandez]

Why

Part 2a of the #1558 stack, on top of #1562. The goal is one read pipeline parameterized by project scope, shared by the project route, the database-scoped route, and MCP search_all_projects. This PR takes full-text execution out of the project-bound repositories and makes every statement the shared read path issues bind the repository's ProjectScope. No query behavior changes.

Part 2b extracts the vector, fusion, relaxation, and chunk-hydration path into a SearchReader the routes can construct without a repository. Splitting keeps this diff reviewable: 2a is scope plumbing and a moved FTS body; 2b is the class extraction and the test-double migration that comes with it.

What changed

• FtsBackend in search_filters: the narrow contract for running a compiled full-text statement on one engine. SQLiteFts and PostgresFts implement it in the backend query modules with the bodies that used to live in each repository's search() and count(). FTS5 syntax errors answer empty. Postgres retries a malformed strict tsquery relaxed inside a savepoint so a caller-owned transaction survives.
• SearchRepositoryBase.search and count are concrete. Shared vector and hybrid dispatch first, then self._fts. Both repositories lose their search(), count(), the pass-through _run_vector_query overrides, and the SQLite entity-column cache, which now lives in SQLiteFts.
• Scope in the read path. Manifest hydration, candidate row fetch, read_manifest_readiness, and classify_hydration_drops take the scope. current_vector_manifest_predicate(scope, params) replaces the :project_id constant; project_readiness uses it for its one project.
• PreparedSearchQuery moves to repository/search_query.py with defaults, so the repository layer can build and pass it. compile_fts_filter takes it instead of thirteen keyword arguments. The service imports it from there.
• The filter helpers both backends share, and the SearchIndexKey alias, move out of the base class into search_filters and search_index_row.
• Test fakes that bypass __init__ set scope beside project_id, and their search() overrides carry the session parameter the base method has. Postgres tests patch the tsquery classifier on postgres_search_query, where PostgresFts reads it.

Kept for 2b on purpose: the best_distance and hasattr(_semantic_vector_index) compatibility branches in the base vector path. About fourteen test files patch _run_vector_query and _ensure_vector_tables on repository instances; those move together with the reader.

Testing

Check	Result
just fast-check	passed
uv run pytest tests/repository tests/services tests/api/v2/test_search*.py tests/api/v2/test_cjk_search_guidance.py tests/mcp/test_tool_search.py --no-cov (SQLite)	1798 passed, 40 skipped
BASIC_MEMORY_TEST_POSTGRES=1 uv run pytest over the search repository, quoted-query, relaxation, temporal, candidate-restriction, rerank pipeline, trace, readiness, and search router suites (testcontainers)	421 passed, 15 skipped
just doctor	passed

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https://claude.ai/code/session_019YW9ysxugGGBCNEGzsxtFV

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