Quick question, why do you keep an installation in the SATA drive anyway? The problem you're having is because there are two EFI partitions (one in each drive) and for some reason the HDD takes precedence over the M.2.

Unless there's some reason to have both systems (for example, one is 7, the other is 10) I would just copy what I need off of the SATA disk, delete all of its partitions, create a single partition and use it for data. No more booting problems, but it may not be suitable if you want to keep both installations.

Aha! I see! I enlarged your screenshot to make it easier to show:



From what I understand, you cloned the contents of one drive onto the other, in that picture I'd saw the disk #0 is the one that came with the laptop and the #1 is the new SSD right?

Those highlighted partitions are system ones, boot ones, they tell the UEFI boot loader what to boot and from where. Once you have installed the OS in the new SSD and made sure the system boots with it, the next step would be to delete everything from the old drive and create a single partition for example.

I say get rid of it all because the HDD still contains the Windows installation that was there before, so you'd be losing some GB in there plus that Recovery partition which is no longer needed either because you have the new one in the SSD.

Let's try something shall we? Let's get rid of the EFI partition in the HDD, leaving it only in the SDD for now and we'll then deal with the rest.

Fire up DiskPart (type it in start and after opening you should see something like this:



Then type "list disk", to see the disks you have and "select disk X" where X is the HDD, you'll know because the HDD is the big one:



To make sure you selected the right one, type "det disk" and it will show you its model and details:



Next, list its partitions with "list disk", you'll see one named as System, that's the one we want to get rid of:



Select that partition with "sel part X" where X is the number and show its properties, to make sure once again it's the one we want:



Now let's delete it, a normal delete command won't do because it is an important partition, we'll have to force its deletion (I won't input the force command because it's my system and I'd have to re-create it otherwise haha):



The command you want to override its deletion is "del part override". ("exit" is the command to exit the program)

If all went well, the HDD should have no EFI partition and it won't be possible for you to boot into the old system. All of your data will still be there, because we just got rid of the partition that was messing things up. Rebooting the machine should make it boot from the only disk that has an EFI partition, the SSD.

I suggest, if at all possible, that you take the data out of the HDD, maybe even to the root of it like... creating a folder called "Data" and putting everything you deem important in there, then getting rid of the rest. You'll gain quite some space in the disk. Ideally the data would have been copied to an external hard disk and then from DiskPart (or any other disk management utility) all of its partitions would be deleted and a new one created spanning the whole disk, but I understand it may not be possible.

By the way, do all of the steps from DiskPart from inside the new system, i.e. use F12 to boot into the SSD and from there delete the EFI partition of the older installation in the HDD. Much more safer. And using the same procedure you can get rid of the Recovery partition that lies in the HDD as well, and stretch the big partition occupying all of the space you just freed (probably easier with the Disk Management, at least it's more visual).