[ERROR] The execution of <<grub-install /dev/sda>> failed. This is a fatal error.

[yancek]

Yes, when I go to the BIOS and go to the boot menu, I get Ubuntu

That's because Mint and several other Ubuntu derivatives use "ubuntu" as the name and directory for an EFI boot. If this was working, selecting ubuntu as you show in your UEFI boot menu would boot Mint.

Have you selected ubuntu in the UEFI menu since you installed Mint? Do you get the same problem? Have you tried going to the BIOS and select boot from EFI file and select the /EFI/ubuntu/grubx64.efi entry? What happens?

Can you use the install USB, boot it and mount the EFI partition on the internal hard drive which shows as sda1 in your boot repair output? You should see several directories there"

Boot HP Microsoft ubuntu

If you don't see those directories, particularly the ubuntu directory, you need to reinstall grub.

[oldfred]

Moved to Mint Sub-Forum.

Mint is not an official flavor of Ubuntu, but uses parts of Ubuntu.
I believe it uses the same boot, so boot entry for 'ubuntu' is really for Mint.