feat: Add FastAPI-style dependency injection system for MCPServer #792

Job	Run time
checks / pre-commit	35s
checks / readme-snippets	12s
checks / test (3.12, lowest-direct, ubuntu-latest)	49s
checks / test (3.10, lowest-direct, windows-latest)	2m 17s
checks / test (3.12, locked, windows-latest)	3m 3s
checks / test (3.12, lowest-direct, windows-latest)	3m 59s
checks / test (3.13, lowest-direct, windows-latest)	2m 37s
checks / test (3.13, lowest-direct, ubuntu-latest)	48s
checks / test (3.14, lowest-direct, windows-latest)	2m 20s
checks / test (3.11, locked, ubuntu-latest)	42s
checks / test (3.10, locked, ubuntu-latest)	51s
checks / test (3.11, lowest-direct, windows-latest)	3m 5s
checks / test (3.11, locked, windows-latest)	2m 19s
checks / test (3.10, locked, windows-latest)	2m 15s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 16s
checks / test (3.12, locked, ubuntu-latest)	57s
checks / test (3.14, locked, ubuntu-latest)	2m 9s
checks / test (3.13, locked, ubuntu-latest)	41s
checks / test (3.14, locked, windows-latest)	3m 2s
checks / test (3.13, locked, windows-latest)	2m 31s
checks / test (3.10, lowest-direct, ubuntu-latest)	47s
checks / test (3.11, lowest-direct, ubuntu-latest)	56s
all-green	4s
	38m 15s

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