I assume you mean 15” 2013 MBP as the 16” didn’t exist until the end of 2019.
As for moving to M1, sure! You might not get any more RAM than what you already had, but the architecture is way more modern than the 2013 15” MBP, which I still have one, and it still works fine, but the M1 would just be way faster.
You do lose hyper threading, but hyper threading is essentially a 1.25X performance boost, so you’d essentially have 5 cores from before, but now with the M1, you’d have 4 high performance cores that are way better than the Haswell i7 chips from 2013 and even the 4 high efficiency cores also perform really well as well.
Plus, you’d get the unified memory (get 16GB), and significantly faster storage as well.
Otherwise, if you can wait a few months, probably hold out for a M1X based chip for the higher end 13” MBP.