It sounds like the third party diagnosis matches the Apple diagnosis.....you have a Logic Board failure. The only difference is that in order to keep finger print recognition, the TouchID must also be replaced since the TouchID can only be paired to a single Logic Board (yes Apple charges you to replace a perfectly health TouchID because of this pairing).
If the third party shop is not an Apple Authorized Service Provider, then how do they plan to fix your Logic Board?
There are three options for them:
- Repair the existing Logic Board by replacing any bad chips or surface mount components on the Logic Board itself....as long as the security enclave chip is not damaged, fingerprint recognition should remain
- Replace Logic Board with a used one which will have a different system serial number. Unless the used Logic Board also includes its paired TouchID, you will lose fingerprint recognition. For some models, the Lid Angle Sensor that was paired with the replacement Logic Board would also be needed so that the position of the Clamshell is properly reported for sleep & wake functionality, although some shops may be able to get a new Lid Angle Sensor they can program a new device someone created in order to get a new Lid Angle Sensor to work with a different Logic Board. Some other macOS functionality could also be impaired if not all parts in the system are properly paired (perhaps dealing with security for streaming videos and Apple Wallet, etc.).
- Maybe the are signed up with Apple's Independent Repair Program to access official Apple parts for some models, but I doubt it since doing so can really hamper an independent repair shop's other services they may provide. I can see that they could forget about the need to also replace the TouchID.
Edit: As for the "Is it worth repairing?" question. I personally would not repair any Apple Intel USB-C Mac. The Intel Macs with the T2 security chip tend to have a higher rate of Logic Board failures than any previous models. And the question still remains how long will Apple and third party developers still keep supporting the Intel platform (usually more of a concern for apps which require Internet access to connect to services)? I'm not sure about the MBAir 2020 Intel model, but I know earlier 2018 & 2019 models had a very poorly designed cooling system. I think the money spent on repairs would be better put towards a replacement laptop.
If you have an M1 laptop, then it may be a bit harder decision to make. I can say that the keyboards on the 2023+ models are much nicer in my opinion as they have a much nicer feel than even the M1 models.
Only you can make the decision as to which option makes the most economical sense to you at this time.
