GE TPG21JRDA side-by-side refrigerator not freezing

Hi, I have a GE side-by-side refrigerator from 2000 (model TPG21JRDA) that has been working constantly with no real issues since I bought it.

However, lately, the freezer hasn't been performing correctly, i.e. frozen items have been thawing. It seems the refrigerator has been getting slightly less cold as well.

Over the past few weeks, I've noticed that:

1. the freezer fan seems to be running all the time (like 24/7), even when the compressor is off
2. there is a click at the end of the compressor's cycle (it clicks with a thud, and the humming from the compressor stops).

Today I removed the front grille and rear panel, and this is what I discovered:

1. the compressor fan is operating intermittently: it will spin for a few seconds, then stop, then spin again, as if the electrical contact were faulty. And whenever the fan spins, it isn't at full speed.
2. (the fan motor was changed about 15 years ago after it got banged while moving it. It started making noise, was changed, and was no issue until now).
3. the compressor is very hot: between 70° and 90° Celsius (160° - 200° F). The compressor fan motor is at 40° C (104° F).
4. when I checked the coils, there was a heavy blanket of dust covering them (I vacuumed it all out obviously)

What I think I understand: The compressor fan isn't performing as it should, so the compressor and coils aren't cooling. The compressor gets hot, shuts down (click sound), before it has a chance to finish the cooling cycle. The freezer fan keeps spinning because it is independent from the compressor (?).

So if I'm correct, the question is: why isn't the fan spinning continuously and at full force?

My guesses:

• there's a short in the fan circuit
• the fan motor is faulty (the fan spins freely though)
• the trigger for the fan is faulty (trigger unit, board?).
• Here's a video of the fan, where the compressor can be heard as well. (With the back panel and its sound-deadening foam, the compressor noise wasn't noticeable at all):
• https://vimeo.com/835245890
• To anybody who understands these better than I do: am I right in thinking that resolving the fan issue will solve the rest? And how do I pinpoint the problem and figure out whether the fan motor is at fault, or electrical units upstream of the fan?