It's a little more than 100€
It's half as much again! If your budget is that flexible you really should have mentioned it in the original post so that people could give you a wider range of options.
Translate it up by a couple of orders of magnitude and you get "I want to buy a car, I have €10,000 to spend" ... "I found one for €15,000, it's a little bit more but ..."
Linux doesn't really know about drives, it knows about partitions and mount points.
Obviously this is a simplification, but in general it's close enough. It also could well be your problem - timeshift doesn't know or care that /boot is on the same physical drive as the rest of your system: if it's a different partition, it's separate.