The 2018-2020 Intel MBAirs with the T2 security chip don't fair very well since they have a very poor cooling system....it doesn't help that these 2018-2020 T2 Logic Boards (in all Mac models) tend have a higher rate of failure anyway than any older models.
About the only things you can try would be a DFU firmware Revive which resets the T2 security chip & system firmware. However, this requires access to another Mac....I don't think Big Sur is good enough for this since later versions of Apple Configurator require later versions of macOS (I think 14.x or maybe even 15.x now). I know I could not do a DFU firmware Revive/Restore using a 2019 Mac with Sonoma on it (even fully patched). I had to install Sequoia on that system in order to be able to perform a DFU firmware Revive/Restore on another Mac even with Apple Configurator. It isn't often where I've seen the DFU firmware Revive actually fix anything at least on the Intel Macs. After performing a DFU firmware Restore on an Intel Mac, you will only be able to reinstall macOS through Internet Recovery Mode (Command + Option + R) because all security settings have been reset to defaults to USB booting is disabled again with no way to re-enable until you reinstall macOS & configure an admin user account.
How to revive or restore Mac firmware - Apple Support
FYI, I don't recommend spending any money on repairs for any of the USB-C Intel Macs for multiple reasons. The money spent on repairs is better put towards a new laptop.
Also, @TheLittles' suggestion of using an external display is a good idea, but it doesn't work as well as it used to do for the older Macs, but it doesn't hurt to try it.