A 2 year old battery could be failing, especially if a "budget" brand.
Sorry to put that back in the mix.
Regretfully I agree, replacement batteries are variable in quality and unless a quality make it could still be the root cause.
Batteries that present as OK can have a single cell at fault and be a big pain to diagnose. I have had this on a few occasions.
Our 2011 car is definitely good for many more years, but I totally understand loss of faith. With this problem, I would do the following in this order
1. Get an alternator test and check the output is good and ask for a repeat test to confirm this. Ask for a short circuit drop test of the battery.
2. Change the earth strap
3. Replace the battery again
4. Get the steering column checked and if necessary refurbished.
When I PX'd out Bravo it was clear it was off to an auction and they were not much interested in it. Just as well as the gearbox was grumbling. When I collected the car they didnt even look at it. I wish I had sent it in without spending anything on trying to sort out its issues!
If you have to pay for the whole lot however its not likely to be economically unviable at c £750 as the car is worth around £2200 - 3000 and px may be less.
A decent Fiat dealer if you can find one should be able to resolve this properly for less than this or at least accurately diagnose the fault. My local one have 100% record of correct diagnosis and guarantee their work. I have found over many years they are the best bet for most jobs I cannot do myself. Fiat dealers are improving and now have better standards targets to meet. Ask them to show you what they have found and explain in detail. My garage seem happy to walk me to the car and explain properly what they have found without any issues. They have even sourced and fitted pattern parts on occasion.