feat: Add FastAPI-style dependency injection system for MCPServer #787

Job	Run time
checks / test (3.11, lowest-direct, ubuntu-latest)	42s
checks / test (3.14, lowest-direct, windows-latest)	2m 20s
checks / test (3.11, locked, ubuntu-latest)	44s
checks / test (3.13, lowest-direct, ubuntu-latest)	47s
checks / test (3.14, locked, windows-latest)	3m 0s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.14, locked, ubuntu-latest)	2m 12s
checks / test (3.10, locked, windows-latest)	2m 30s
checks / test (3.11, lowest-direct, windows-latest)	2m 13s
checks / pre-commit	24s
checks / test (3.13, lowest-direct, windows-latest)	3m 35s
checks / test (3.10, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, locked, ubuntu-latest)	54s
checks / test (3.10, locked, ubuntu-latest)	45s
checks / test (3.13, locked, ubuntu-latest)	45s
checks / readme-snippets	11s
checks / test (3.10, lowest-direct, windows-latest)	2m 19s
checks / test (3.12, lowest-direct, ubuntu-latest)	51s
checks / test (3.13, locked, windows-latest)	2m 16s
checks / test (3.12, lowest-direct, windows-latest)	3m 40s
checks / test (3.11, locked, windows-latest)	2m 30s
checks / test (3.12, locked, windows-latest)	3m 37s
all-green	5s
	38m 23s

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