What's 'repairable' 🤔

I have a 9 year old system.
topped off 2 lbs of refrigerant and 3 weeks later freezing over again.

First guy recommended a new system

2nd company I called to do the leak check tried to bail after 20 mins and didn't even check indoors until I asked. Revealed that we have two leaks. One on outer coil and one inside. Maybe more, I don't trust them much and they didn't point out anything but general coil areas.

I'm not the original owner so I'm screwed on warranty.

They also didn't check any of the lines, so I'm curious if that's normal on a leak check?
Can you repair coil leaks or not worth?