Sounds like the Logic Board has failed assuming the power supply is Ok. At least you received a somewhat useful error message....I have never received any useful error messages when a "Restore" fails. Your only option is to attempt the "Restore" process which will destroy all data on the Mini's internal SSD. AFAIK there is no way to access the data on the internal SSD unless perhaps a professional data recovery service such as Drive Savers has some secret tricks for accessing the data.
In my recent experience, it seems these 2018+ Mac Minis and iMacs seem to have the Logic Board as the weakest link these days since Apple decided to integrate everything into them instead of having separate removable components. It doesn't help that the security enclave complicates things tremendously and Apple is so secretive about everything. I've had to replace a lot of Logic Boards in these 2018+ desktop models....I've never had to replace Logic Boards in any of the pre-USB-C iMacs & Minis so this is a very disturbing trend for me.
I hope you at least have good backups.