@clUB28 Ok, I will try and point you in the direction of sorting this out.

Try this first. Open a terminal where your fastboot and adb drivers are, have the device in fastboot mode (the bootloader).
The Pixel 3a has slots, slot a and slot b. In fastboot try this command:

fastboot --set-active=a
Then boot the device.
If that fails, try:

fastboot --set-active=b
Then boot the device.

If that fails, reinstall Android and start again. I have done the below on my Ubuntu machine as well as Windows 10 and 11. (Chrome Browser, not Chromium is required)

You have to have the phone on the stated version of Android in the installer: PQ3B.190801.002

Link to this.

Your bootloader has to be unlocked.
Use the Android Flash Tool addon and Google Chrome to flash your device to the correct Android ROM - Choose the Flash link. It is the easiest way and clearest way if you have not done this before.

Do this when installing the ROM (just before):

Force flash all partitions - ticked
Disable verification - ticked
Disable verity - ticked

It is in the menu on the Android Flash tool. This will stop the device hanging at the Google logo.

Once You have installed Android and set it up, then go through the UT Installer procedure.

If you are OK on the command line and you wish to try with out Chrome have the device connected in fastboot mode to the PC and download the Link ROM rather than the Flash, extract it, open a terminal in the folder and run the flash-all.sh,