Someone who can guide me ...?

Friends, I'll tell you about my Jetta A4, 2.0L automatic.
It started doing this: when passing, the car wouldn't shift from 3rd to 4th; it would stay in 3rd. My transmission mechanic said we'd tune it up and replace the valve body. The oil came out clean, with no residue.
The problem persisted, and it only happens occasionally. Of course, I paid him for the work, but my car is still doing it. It stops if I stop for a couple of minutes, turn it off, and that's it.
Then it happened again, so I took it back to the mechanic for a checkup. The oil light came on, and the warning chime sounded. My mechanic said it was probably a sensor that had come loose. I continued driving it like that, and then my car sounded like a diesel...
so now they're telling me it's the oil pump, and in the worst-case scenario, the bearings too.
I've already taken the oil pan apart; I want to fix it myself since I don't have much money to take it to a shop.
Can anyone tell me if the oil pump needs to be serviced after removal?
And also, I checked, and the oil strainer is clogged.

Hey man, look, oil pumps are usually installed on the vehicle's timing belt or connected to the camshaft, etc. They're not usually timed unless they drive two or more gears. I mean, they're installed as a pump and also as an idler gear, transferring power to another gear.
If that's not the case and it's just located at the bottom of the oil pan, just remove it along with the oil pickup (make sure everything is washed and clean before reassembling). The pickup sometimes has an O-ring or gasket, and don't risk it with the pump; just replace it. Check the bearings; one might have rotated. Hope it works out for you.

I already changed the oil pump, and now, following your advice and that of other friends, I've removed one of the connecting rod bearings to check for damage. It's not completely worn, but the wear from use is noticeable. I'm about to ask a mechanic for his opinion on whether to replace them now or start the complete reassembly. The only problem is, I've been looking for the correct torque for the connecting rods and can't find it. I once heard it was 22 ft-lb plus 1/4 turn. If anyone on the forum knows this information, it would be a great help in confirming or clarifying it.
Thanks, Marcelo, for your information.
Regards

Hi again. Regarding the metal parts, some wear is normal, but if I were you, I'd replace them without hesitation. They're not that expensive. Buy the same size you're using. On one side of the metal, it will say if it's STD (standard) or .25/0.50, etc.
These are the measurements it has after being machined. But just in case, take the old part with you and buy the correct size. It's important to pay attention to the notches on the metal parts when you disassemble it for reassembly. Make sure the notches are in the same place. For example, the connecting rod has a small recess where the notch goes towards the back of the engine. The connecting rod cap should also be the same. Just make sure the surfaces are clean, place the metal parts, and before assembly, lubricate them a little with clean oil and torque to 70 FPS plus 1/4 turn on the connecting rod. Apply silicone to the crankcase and engine gaskets, and you're done. (For a good result, wash the parts with 93 octane gasoline.) Cheers, man, hope it turns out great!