Summary

• Adds public ClientSession.register_tool_schema(name, output_schema=None) so dynamically discovered tools (absent from list_tools()) can populate the output-schema cache without touching private _tool_output_schemas.
• Mirrors the same helper on high-level Client.
• Keeps the compiled validator cache consistent: a changed registration evicts the compiled validator (same _same_schema check as _absorb_tool_listing).
• Documents interaction with complete list_tools(): an uncursored single-page listing still prunes schemas for tools not in that listing (including manual registrations); re-register if still needed. A listing that includes the name replaces the registered schema.

Fixes #3145

Motivation

Servers that use search/catalog-style discovery (e.g. Bedrock AgentCore Gateway) intentionally return only a small list_tools() subset. Invoking discovered tools today logs a warning and skips structuredContent validation unless callers write the private cache. This PR adds the small public API proposed in the issue.

Design notes / ask for review

Issue #3145 is unlabeled (ready for work not present). Claimed on the issue; happy to adjust API/prune semantics if maintainers prefer a different contract (e.g. surviving complete listings). Preferring a ready PR over draft for reviewability.

Test plan

• uv run --frozen pytest tests/client/test_register_tool_schema.py tests/client/test_session_promotions.py -q
• uv run --frozen ruff check / ruff format --check on touched files
• uv run --frozen pyright on touched modules
• CI on the PR

AI disclosure

Implemented with AI assistance (Cursor). I reviewed and understand the full change, including validator-cache eviction and the documented list_tools() prune interaction.