I don't think I can usefully comment on the quality of the guitar or its hardware simply on the basis of the recordings. There are too many possible factors that could affect the recorded tone.
In general, my opinion is that the Fender Squier guitars are excellent value for the money. I love the Telecaster vibe, though I myself own a Squier Stratocaster that I bought secondhand a couple of years ago. It's about 20 years ago, but after a set-up, it played great.
I thought the stock pickups (which were ceramic) were a bit aggressive and bright for my taste, so I replaced them with Alnico pickups (though still single-coils) made by a local luthier.
I would suggest taking your Telecaster to a luthier (perhaps a different luthier than the one who fixed it for you recently) and get their opinion.
Guitars with single-coil pickups can be noisy -=- and they can be extra noisy when recording on a computer in comparison with playing through a traditional amp (because of all the additional electromagnetic interference that a computer and its electronics can generate). Thus, to some extent, I would not go into shock if the guitar sounded noisier when you are using it with your computer. But, also, you might be able to get a luthier to shield the electronics, etc. which can help with (if not always eliminate) such problems.