feat: capture MCP protocol logging notifications in server connection logs #283

Job	Run time
ts-check	2m 56s
rust-check	2m 10s
rust-test (ubuntu-latest, x86_64-unknown-linux-gnu)	3m 37s
rust-test (macos-latest, aarch64-apple-darwin)	3m 36s
rust-test (windows-latest, x86_64-pc-windows-msvc)	5m 24s
coverage-report	8s
e2e-web	2m 8s
e2e-desktop / e2e-desktop (windows-latest)	22m 55s
e2e-desktop / e2e-desktop (ubuntu-latest)	17m 3s
test-report	13s
e2e-desktop / e2e-report	7s
	1h 0m 17s

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