The symptoms you described was telling me a bad Logic Board was likely. There won't be any diagnostics test results since the laptop won't power on. All there would be to report are just several steps they performed to attempt to power on the laptop including SMC Reset, trying each USB-C port to power the laptop, attempting a firmware "Restore" of the laptop. Possibly disconnecting the battery. I know I would disconnect the I/O Boards and test with a known good I/O Board since many of the laptops I support have liquid damaged USB-C ports. This is usually enough to confirm a bad Logic Board, but I personally also try disconnecting the built-in display, keyboard & trackpad just on the off chance one of these items is a problem just to see if a "ding" occurs when connecting the charger or if the heatsink gets warm since I've seen so many odd quirky things with these laptops, but these Macs also don't like to have these components disconnected.
Graphical glitches are just one sign of a bad Logic Board when there is a GPU failure or possibly a memory failure since some memory failures can result in graphical glitches as well.
The only way an AASP could possibly attempt data recovery is if the laptop can be put into DFU Mode, but even if successful, the data transfer requires a service provider only utility and the transfer only occurs over a USB 2 cable which has a max transfer rate of about 50MB/s, so it could take days to transfer the data. However, not all AASPs will provide this service and it will cost extra. Besides, if the tech attempted a "Restore" of the system firmware (one of the troubleshooting steps for these symptoms), then the data on the internal SSD may already been destroyed. Keep in mind Apple puts the responsibility of user data on the user and assumes the user is taking advantage of the built-in Time Machine software to backup the computer. Apple does not do data recovery and does not require AASPs to do so either.
You can try having Drive Savers to attempt data recovery, but there are no guarantees since the data on the internal SSD is hardware encrypted with the T2 security enclave holding the encryption keys. Drive Savers does provide a free estimate and are recommended by Apple. However, if you are going to have Apple or the AASP repair the laptop, then you will need to talk with the AASP about how to go about with Drive Savers attempting data recovery before the repair is performed. Years ago, the AASP would send the drive to Drive Savers on your behalf during the repair since the AASP needs to return the bad part to Apple after the data recovery attempt & repair. I don't know how they do this now when the whole Logic Board is involved, but you should make sure to co-ordinate with the AASP to make sure how this process is supposed to work.
People should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. There are a lot more ways to lose data with these newer computers since it is nearly impossible to recover data from these newer Macs and even hardware encrypted SSDs. Many times there will be no warning signs when a failure occurs....failures can be sudden.
