C4480 (almost identical to C3180) says “Out of Paper”—but it’s not

Check the rollers for extreme amounts of free movement and wear. Some movement is fine on these, but it should come with a lot of resistance. If it spins all day long, one of the gears on the pickup is broken, effectively totaling the printer unless it's just loose and can be reinstalled. That said, the odds are higher that it's broken and will not be easily reinstalled, given that HP uses cheap ABS plastic, which tends to crack under repeated stress on these printers. If there is a big part that is worn out to such an extreme, it is an outlier spot; the roller itself is bad. The problem is servicing it is impossible, something like Rubber rejuvenator can be used to EXTEND the remaining lifespan -- not repair, it just buys you time.

If the rollers are good, cheap paper with little to grip is another notorious cause for this, given how slippery the mechanism is on cheap printers like this. Use 24lb stock, or good paper like Hamermill. This can also help compensate for wear and tear, if there is wear that's bad enough to show but not so far gone that you need to give it an assist, like with a rubber rejuvenator.

If the printer is bad, buy a Canon or basic monochrome laser unless you need color. New HPs from 2015+ are "infected" with HP DS and HP+, and HP+ is straight-up "opt-in" vendor lock-in by requiring genuine HP ink that gets enabled when you use an HP account. That's all it takes.