feat: Add FastAPI-style dependency injection system for MCPServer #781

Job	Run time
checks / pre-commit	36s
checks / readme-snippets	12s
checks / test (3.13, locked, ubuntu-latest)	47s
checks / test (3.13, locked, windows-latest)	2m 19s
checks / test (3.12, locked, windows-latest)	3m 28s
checks / test (3.13, lowest-direct, ubuntu-latest)	49s
checks / test (3.13, lowest-direct, windows-latest)	2m 28s
checks / test (3.14, lowest-direct, windows-latest)	2m 26s
checks / test (3.11, lowest-direct, ubuntu-latest)	43s
checks / test (3.10, locked, windows-latest)	2m 15s
checks / test (3.11, lowest-direct, windows-latest)	2m 35s
checks / test (3.12, locked, ubuntu-latest)	52s
checks / test (3.10, lowest-direct, windows-latest)	2m 53s
checks / test (3.11, locked, windows-latest)	2m 41s
checks / test (3.14, locked, windows-latest)	3m 7s
checks / test (3.14, locked, ubuntu-latest)	2m 14s
checks / test (3.12, lowest-direct, ubuntu-latest)	51s
checks / test (3.12, lowest-direct, windows-latest)	3m 43s
checks / test (3.10, lowest-direct, ubuntu-latest)	49s
checks / test (3.11, locked, ubuntu-latest)	47s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 10s
checks / test (3.10, locked, ubuntu-latest)	47s
all-green	8s
	38m 40s

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