Convert `sync_back.py` to TypeScript #11584

Job	Run time
analyze-other (actions)	50s
analyze-other (python)	59s
check-codeql-versions	10s
analyze-javascript (windows-2022, linked)	7m 3s
analyze-javascript (ubuntu-24.04, linked)	4m 17s
analyze-javascript (macos-14, linked)	5m 55s
analyze-javascript (windows-2025)	10m 28s
analyze-javascript (ubuntu-24.04)	4m 46s
analyze-javascript (macos-14)	5m 40s
analyze-javascript (windows-2025, linked)	7m 45s
analyze-javascript (ubuntu-22.04)	5m 4s
analyze-javascript (macos-15)	6m 0s
analyze-javascript (macos-15, linked)	7m 2s
analyze-javascript (windows-2022)	6m 7s
analyze-javascript (ubuntu-22.04, linked)	4m 28s
	1h 16m 34s

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