It’s real. Here’s an article. There are numerous 50+ people re-upping.
Some out of duty, some because their retirement isn’t sufficient.
I’ll bet they’ll make very good soldiers. Even if not on front line they can work support and free younger soldiers for more active duty.
https://www.military.com/daily-news/2020/09/12/59-year-old-army-bct-grad-about-be-new-guy-his-sons-unit.html
Just do a quick search. All branches are looking.