feat: Add FastAPI-style dependency injection system for MCPServer #789

Job	Run time
checks / pre-commit	37s
checks / test (3.11, locked, ubuntu-latest)	45s
checks / test (3.10, locked, windows-latest)	15m 1s
checks / test (3.12, locked, ubuntu-latest)	50s
checks / test (3.14, locked, ubuntu-latest)	2m 18s
checks / test (3.13, locked, windows-latest)	2m 17s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / test (3.13, lowest-direct, windows-latest)	2m 46s
checks / readme-snippets	14s
checks / test (3.13, lowest-direct, ubuntu-latest)	51s
checks / test (3.11, locked, windows-latest)	2m 18s
checks / test (3.12, lowest-direct, ubuntu-latest)	49s
checks / test (3.10, lowest-direct, ubuntu-latest)	51s
checks / test (3.12, lowest-direct, windows-latest)	3m 17s
checks / test (3.14, locked, windows-latest)	3m 37s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 12s
checks / test (3.11, lowest-direct, windows-latest)	2m 40s
checks / test (3.10, locked, ubuntu-latest)	46s
checks / test (3.12, locked, windows-latest)	3m 14s
checks / test (3.10, lowest-direct, windows-latest)	3m 7s
checks / test (3.11, lowest-direct, ubuntu-latest)	46s
checks / test (3.14, lowest-direct, windows-latest)	2m 18s
all-green	5s
	51m 28s

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