Relay loud tick every minute or two, but fridge is working

I have a 14 year old Whirlpool fridge that has been making a loud clicking noise every minute or two and seems to be running all the time. The freezer and fridge has been remaining cold, i.e. not totally broken.

I pulled the fridge out, noticed the fan near the condenser was working fine. Took the panel off the back and saw that the coils had a couple places with heavy dust but really not too bad.

The large black compressor seemed pretty hot, I’m not sure how hot they’re supposed to get, and I didn’t take any measurements of the copper pipes, but I can say that the round compressor itself was hot enough that leaving my hand on it for more than a few seconds was getting uncomfortably warm (i.e. didn’t ‘burn’ me, but a bit painful to leave on for too long).

I took the relay off and shook it. There is a very slight noise I can hear if I shake it the right way, but nowhere close to what I see on videos where people say: “this is what a bad relay sounds like”.

My questions are:

If the compressor is hot as described above, does that mean it’s working too hard / constantly cycling / staying on? Wasn’t sure if it’s normal for the exterior wall of the compressor to be hot like that.

If it’s working overtime, can the relay be bad? Or would a bad relay mean that the compressor would never work at all?

I was going to order a replacement relay, but if it can’t be a bad relay (because the compressor is working, even though it seems to be “overworked”), then I don’t know that I really want to order one.

Thanks!

I’m still hoping someone has suggestions on this. Any advice?