Refactor: Restructure MCP Server Implementation for Better Modularity #5951

Job	Run time
check-translations	43s
compile	1m 27s
check-openrouter-api-key	1s
knip	53s
test-extension (ubuntu-latest)	2m 5s
test-webview (ubuntu-latest)	1m 49s
test-extension (windows-latest)	3m 6s
test-webview (windows-latest)	3m 38s
integration-test	0s
unit-test	1s
	13m 43s

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