feat: Add FastAPI-style dependency injection system for MCPServer #795

Job	Run time
checks / readme-snippets	18s
checks / pre-commit	29s
checks / test (3.13, lowest-direct, ubuntu-latest)	51s
checks / test (3.11, lowest-direct, windows-latest)	2m 24s
checks / test (3.13, locked, ubuntu-latest)	1m 3s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.11, lowest-direct, ubuntu-latest)	53s
checks / test (3.14, locked, windows-latest)	3m 13s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 18s
checks / test (3.13, locked, windows-latest)	2m 18s
checks / test (3.11, locked, ubuntu-latest)	55s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
checks / test (3.10, locked, windows-latest)	2m 15s
checks / test (3.10, lowest-direct, ubuntu-latest)	53s
checks / test (3.10, lowest-direct, windows-latest)	2m 23s
checks / test (3.13, lowest-direct, windows-latest)	2m 28s
checks / test (3.12, locked, ubuntu-latest)	52s
checks / test (3.12, lowest-direct, windows-latest)	6m 6s
checks / test (3.12, locked, windows-latest)	3m 8s
checks / test (3.10, locked, ubuntu-latest)	51s
checks / test (3.11, locked, windows-latest)	2m 56s
checks / test (3.14, lowest-direct, windows-latest)	3m 11s
all-green	3s
	42m 8s

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