Google knows whether your content is recent or not regardless if you have a timestamp on it, because they crawl periodically and according to recent leaks they do store this information.
It's hard to tell if they use it. Most of SEO is just cargo-culting because of how difficult it is to experiment with it. Somebody once said it helped them to remove the date, and now everyone does it. Maybe google is using it, or was using it at some point. Maybe they use the date in structured data [1] because it's easier to get and potentially more reliable (telling content changes and theme changes apart isn't trivial), and people just noticed that if they turn off the date feature in their CMS their articles rank better.
Unfortunately, it's not hard to make a few tweaks though and have it look "updated" to the crawler. I imagine Google could change that (especially now with LLM tech possibilities) so I guess we'll see what happens, but so far it hasn't hurt the career "optimizers" that I know.
