Refactor: Restructure MCP Server Implementation for Better Modularity #5950

Job	Run time
check-openrouter-api-key	1s
compile	1m 23s
check-translations	48s
knip	1m 1s
test-extension (ubuntu-latest)	1m 54s
test-webview (ubuntu-latest)	1m 30s
test-extension (windows-latest)	3m 29s
test-webview (windows-latest)	2m 51s
integration-test	0s
unit-test	1s
	12m 58s

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