OS 11 install. No writable disk Permisson denied...

The previous owner wanted to reinstall big sur. A mistake was probably made in the process. The installation process is canceled: permission denied.

My trials: Installation via recovery mode (network boot, since no recovery is available on the SSD), via target mode, via USB-C with an external installation volume.

First aid with disk utility and terminal. All levels of container disk 1 and the SSD, top level. Exit code 66, error -69845, -69716.

Same same when trying to delete the volume. Error -69623, -69845, a writable volume is required Error -69772.

Informations I have found

Although Big Sur uses the same protected system volume and APFS volume group as Catalina, it changes the way the volume is protected to make it even more of a challenge for those who use malicious software Develop: Welcome to the Signed System Volume (SSV).

Every file on Big Sur's system volume now has a SHA-256 cryptographic hash that is stored in the file system's metadata. When data is read from the SSV, its current hash is compared to the stored hash to ensure that the file has not been tampered with or damaged.

It would be great, if anybody had ideas to fix my problem : )