Hi
We had an old MacPro which was stuck at 10.11. We were not able to update Photoshop and Lightroom for years.
But...we kept paying our monthly fee because Photoshop and Lightroom had vastly greater functionality than Photoshop Elements. (Bear in mind you will be stuck with an older version of Photoshop Elements too.) And the older version of Photoshop and Lightroom, while lacking all the updates, was nevertheless adequate for our needs.
Historical note: we recently upgraded our hardware to a MacStudio and are not enjoy all the new features of Photoshop and Lightroom. It is quite amazing what these programs can do now.
You are going to have to update that old computer someday. Your browsers and other programs are increasingly out of date already.
So tough it out as long as you can with the old hardware and then make the move to new hardware.
Good luck.