yeah, your derailleur will manage a 12 tooth gap (44-32) and maybe 14 BUT, there are other things to consider...
Does your current derailleur afix to the frame with a clamp around the seat tube, or directly to the seat tube (this is known as a "braze-on)?
It's a clamp so no issues there.
Is your bottom bracket a cartridge type or cups?
Cartridge (FSA).
What brand is the current groupset?
It's a mish-mash of Shimano, Sunrace, and FSA - basically built to a price point
Do you have the tools and skills to do this yourself?
Yeah, no problem. Been building bikes since my teens.
What tools and knowledge I lack I can borrow from a friend up the street who has the whole kit (ex pro racer).
$64,000,000 question (I know the answer's not $64,000,000)... how much do you want to spend before you chuck the bike in the skip and buy a more appropriate one?
My ideal would be to build a new road bike but parts availability is limited, so my current plan is to buy parts for this bike and then eventually swap them over to a road bike frame and revert this one back to a general bike.
Important point...with your new cassette I think you will need to shorten your chain if you leave the chainrings the same.
www.machinehead-software.co.uk
Take 3 links out.
It should be fine as the smallest cog is the same and the largest cog is smaller than the current largest cog, so it's in the same range.
However, the chain seems overly long as it is so I think I will drop a few links anyway.