Disk is not convertible to APFS

It appears that you have erased your drive completely, before allowing booting from an external drive.

In this situation you will need to install using Internet Recovery. It will be slow.

If the drive is now empty, you should go into Disk Utility, select the whole drive (not just a volume, the drive itself; you may need to click View and make sure that Show All Devices is checked). Erase as APFS with GUID partition table.

Choose any name you like, then click Erase.

Quit Disk Utility and start the installation.

When you do so, the available possibilities are the current OS or the OS that originally shipped with your mac. I am guessing that is why you got Mojave before.

Complete the installation. Boot from the system just installed. Check whether or not the drive is now APFS (it should be).

Make sure that your account is an administrator.

Restart from Recovery (it should be faster now, as it will use the Recovery partition in your drive), go to Startup Security and enable booting from an external drive.

Make a bootable installer on a usb thumb drive. Boot from this installer disk by holding down the Option key when you start your mac. Before proceeding with the installation erase the internal drive as APFS eith GUID partition table.

“reinstall “?

Are you sure you booted from the usb installer disk and not from the recovery partition?

Option key on startup; when the options for booting appear on screen choose the usb drive; using disk utility erase the whole internal drive (not just individual volumes); quit disk Utility and install. The word “reinstall” should not appear here. I cannot see any other way it might appear unless when booting from recovery. This might install Mojave if it was the original system this mac came with.

Are you saying that you ran Startup Security Utility (which can only be run from the Recovery partition), tried to enable booting from an external drive and it said there was no administrator account? That’s weird. Can you boot into Mojave and check if your account has admin privileges?

nzoo wrote:

I tried this, completely erasing the disk, when installing mojave or catalina two minutes before the end of the installation, an error appears in the installer log: Disk is not convertible to APFS and the computer restarts.

Weird!!!... if the drive had already been erased and formatted as APFS...

nzoo wrote:

Thanks for the answer! Is this any different from the disk utility I use in the command + R "process"?

Try it and see— report back you findings.