This is going to be a bit longer, so I am unable to post it as a comment.
You have three drives attached to your system.The first drive
sda has two partitions, sda1 is a
Microsoft reserved partition, maybe a leftover from a former Windows-installation on the drive.
sda2 is a NTFS-partition, data-storage.
The drive has a GPT-partition-table.
On your second drive
sdb your recent Windows is installed in UEFI-mode, ESP-partition
sdb1 is on this drive. GPT-partition-table.
On your third drive
sdcyou just installed Ubuntu, but in legacy-mode, this is the point creating your headache. You should have installed in UEFI-mode.
The drive has MBR-partition-table.
You should convert this drive from MBR to GPT, you can use Gparted to do that.
Then install Ubuntu again, but install in UEFI-mode. You have to boot the installer in UEFI-mode to do that, how you boot is how it installs.
Grub will be installed on the ESP-partition off the internal drive. By default Grub will be installed on the ESP of
sda. This fact leads to the next issue.
The ESP-partition should be on the first drive
sda, but just right now it is on the second drive
sdb. That may lead to boot-problems.
I don't know if it is possible to change the drives in your laptop, that would solve this issue. If the second drive is an external drive too, then you have to leave it as it is.
Before doing all that you may try the suggested repair by running Boot-repair again (click
recommended repair-button) and see if it works properly.
I have my doubts...
I found this and that leads me to another idea.
You want to install in UEFI-mode, but you don't want your Windows-drive to be affected in any way. You may try this:
Detach the Windows-drive from the Laptop. Install Ubuntu on the external drive in UEFI-mode. Create ESP-partition on this drive during install (ca.500MB FAT, boot-flag). After install finished reattach the Windows-drive.
Boot to external drive to start Ubuntu, run
sudo update-grub, so the OS-prober can find Windows and creates Grub-menu-entry. Set boot-order in UEFI-BIOS to external drive. In the case the external drive is not attached you would have to change boot-order to Windows-drive.
No warranty, I can't test that due to missing equipment. But here you can see that I am not the first with this idea...