Check the back of the printer for a sticker with the manufacture date.
Depending on usage & other factors, these low-spec printers do have a finite life span.
If you're a tinkerer and mechanically handy (which I am not), you *may* be able to get to the rollers to "fix" them, at least temporarily.
As for failure to print the Test Page, that (like it or not) could be due to using non-HP cartridges, or due to clogged ink nozzles or other issues.
And then there are driver/software compatibility issues. The OEMs do not provide updated drivers forever - doing so would be expensive for them & they would rather sell you a new printer.
Bottom line: decide how much time/effort you want to expend trying to resuscitate this old printer vs. cost of a new, Win11 (& beyond) compatible printer.
Just my two cents and worth less
Yeah I'll probably buy a new one. I spent my life building and fixing things, I'm retired now and have zero interest in fixing anything anymore.