feat: implement configurable tool container home directory

- Add ToolType.home_directory column with default /home/user
- Add Alembic migration to add column, set existing rows, and rewrite
  /workspace to /home/user/{{WORKSPACE_NAME}} in legacy templates
- Add merge migration fc8f1a20cbf6 to resolve Alembic multiple heads
- Update manifest compiler to honor manifest.home_directory for HOME,
  WORKDIR, /workspace symlink, and default repo mount target
- Update legacy dockerfile/compose instance generation to use
  tool_type.home_directory
- Thread resolved home_dir through config profile and git mount expansion
- Generate entrypoint permission fixer to chown home/mounts at startup
- Update base.dockerfile with sudo/passwordless sudo for permission fixer
- Add unit tests for manifest compiler, instance service, and migrations
- Add placeholder integration test for container lifecycle
- Update openspec/tasks/home-path-expansion.md task checkboxes
- Update project maps for modified files

Quality gates: py_compile, ruff, mypy, pytest tests/unit (205 passed),
pytest tests/integration (110 passed, 35 skipped). Alembic round-trip
and container lifecycle integration tests require Docker/PostgreSQL.

apps/api/alembic/versions/.pi-map.index.md

@@ -2,7 +2,7 @@
 dir: apps/api/alembic/versions
 
 ## role
-Contains sequential Alembic database migration scripts that evolve the API's relational schema over time, tracking structural changes from initial tables through complex features like tool instances, config profiles, workspaces, manifests, and monitoring.
+Database schema evolution and versioning management for the API application using Alembic migration scripts.
 ## parent
 index: apps/api/alembic/.pi-map.index.md
 map: apps/api/alembic/.pi-map.md
@@ -48,6 +48,7 @@ map: apps/api/alembic/.pi-map.md
 - 2026_05_29_remove_ssh_keys_mount_from_manifest.py
 - 2026_06_01_add_workspaces.py
 - 2026_06_13_make_clone_mode_nullable.py
+- 2026_06_14_104415_add_tool_type_home_directory.py
 - 398082499c30_add_tool_config_fields.py
 - 6fc7bfcf199f_merge_remove_is_builtin_and_add_config_.py
 - 86cec91fdb00_merge_profile_resolver_and_workspaces_.py
@@ -55,6 +56,7 @@ map: apps/api/alembic/.pi-map.md
 - 8ed7dd80973d_create_config_folders_table.py
 - af8512103d67_add_tool_type_fields.py
 - f3d2dc90ba3a_merge_single_interface_and_clone_mode.py
+- fc8f1a20cbf6_merge_home_directory_and_pi_agent_mount_.py
 ## links
 index: apps/api/alembic/versions/.pi-map.index.md
 map: apps/api/alembic/versions/.pi-map.md