feat: Add FastAPI-style dependency injection system for MCPServer #783

Job	Run time
checks / pre-commit	25s
checks / test (3.11, lowest-direct, windows-latest)	2m 41s
checks / test (3.10, lowest-direct, windows-latest)	2m 27s
checks / test (3.11, locked, ubuntu-latest)	47s
checks / test (3.12, lowest-direct, windows-latest)	3m 18s
checks / test (3.11, lowest-direct, ubuntu-latest)	46s
checks / test (3.13, locked, windows-latest)	2m 19s
checks / test (3.12, locked, windows-latest)	3m 39s
checks / test (3.13, locked, ubuntu-latest)	46s
checks / test (3.11, locked, windows-latest)	2m 28s
checks / test (3.10, lowest-direct, ubuntu-latest)	51s
checks / test (3.12, locked, ubuntu-latest)	47s
checks / test (3.12, lowest-direct, ubuntu-latest)	52s
checks / test (3.13, lowest-direct, ubuntu-latest)	44s
checks / test (3.10, locked, ubuntu-latest)	46s
checks / test (3.14, lowest-direct, windows-latest)	2m 16s
checks / test (3.14, locked, windows-latest)	3m 9s
checks / test (3.13, lowest-direct, windows-latest)	3m 4s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.10, locked, windows-latest)	2m 11s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
checks / readme-snippets	15s
all-green	4s
	38m 2s

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