For example, take this NYT article https://www.nytimes.com/2022/08/31/health/life-expectancy-co...
Google cache:
https://webcache.googleusercontent.com/search?q=cache:https:... -- 404
OP's service
https://cfworker-beatthatwall.jayass.workers.dev/?url=https:... -- works.
However, one can adopt your bookmarklet to use OP's service when needed instead of installing extension/userscript that seem to match all the sites.