Fix server lifespan overlap teardown

[jlowin]

Motivation

• Server-level lifespan was tracked by a simple boolean and cleared on any exit, which allowed overlapping in-process client sessions to prematurely tear down shared resources and cause intermittent failures.

Description

• Add a reference count and lock (_lifespan_ref_count, _lifespan_lock) to FastMCP and make _lifespan_manager increment/decrement the ref count under asyncio.Lock to serialize entry/exit.
• Ensure the first entrant initializes the user lifespan and provider lifespans, while additional entrants only increment the counter and yield without re-entering teardown logic, and ensure teardown runs only when the final session exits.
• Add a focused regression test test_server_lifespan_overlapping_sessions that keeps one client alive while another exits and asserts the shared lifespan resource remains open until the last session closes.
• Files changed: src/fastmcp/server/server.py, src/fastmcp/server/mixins/lifespan.py, tests/server/test_server_lifespan.py.

Testing

• Ran uv sync successfully to ensure deps were available.
• Ran the focused lifespan tests with uv run pytest tests/server/test_server_lifespan.py -n auto and they passed (17 passed).
• Ran the full test suite with uv run pytest -n auto; there were unrelated flaky/timeouts in this environment (11 failed, 1 error) that are not related to the lifespan refcounting change.
• Ran lint/type checks for modified files with uv run ruff which passed; uv run prek run --all-files failed to initialize hooks due to an external network-retrieval error and is not a code regression.

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Codex Task

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Clear lifespan state when non-owner context is last to exit

When the first-entered session exits before a later overlapping session, teardown runs in the owner branch, but this non-owner branch only decrements _lifespan_ref_count and returns. If that decrement reaches zero, _lifespan_result_set remains True (and _lifespan_result stays stale), so subsequent sessions take the fast path and skip re-entering lifespan entirely even though resources were already torn down; this leaves future requests running against closed/uninitialized lifespan state.

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[jlowin]

Auto-reviewed: all CI checks green, review comments addressed. Merging.