feat: Add FastAPI-style dependency injection system for MCPServer #786

Job	Run time
checks / pre-commit	20s
checks / readme-snippets	16s
checks / test (3.10, locked, windows-latest)	2m 16s
checks / test (3.12, locked, windows-latest)	3m 8s
checks / test (3.10, lowest-direct, windows-latest)	2m 16s
checks / test (3.10, lowest-direct, ubuntu-latest)	48s
checks / test (3.13, locked, windows-latest)	2m 31s
checks / test (3.12, lowest-direct, ubuntu-latest)	52s
checks / test (3.11, lowest-direct, windows-latest)	2m 39s
checks / test (3.11, locked, windows-latest)	2m 22s
checks / test (3.14, lowest-direct, windows-latest)	2m 21s
checks / test (3.13, lowest-direct, windows-latest)	2m 32s
checks / test (3.13, locked, ubuntu-latest)	45s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 7s
checks / test (3.11, locked, ubuntu-latest)	46s
checks / test (3.14, locked, ubuntu-latest)	2m 18s
checks / test (3.12, lowest-direct, windows-latest)	3m 5s
checks / test (3.10, locked, ubuntu-latest)	46s
checks / test (3.13, lowest-direct, ubuntu-latest)	46s
checks / test (3.14, locked, windows-latest)	3m 40s
checks / test (3.11, lowest-direct, ubuntu-latest)	45s
checks / test (3.12, locked, ubuntu-latest)	57s
all-green	4s
	37m 20s

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