The problem is almost certainly not with the derailleur itself. It's probably badly adjusted (sounds like you have too much slack in the shift cable). Another issue that leads to bad shifting is the cable may be sticking in the housing.
Checking for a sticky is easy, with the bike off the ground, shift to the big ring and then down to the small ring while watching the derailleur. If it does not move as soon as the the cable is sticking. Remove it, clean and lubricate or replace along with the housing.
Work through a step-by-step front derailleur adjustment process (you'll need to do this if you replace the cable or derailleur anyway).
Shimano very helpfully published their specifications here: https://productinfo.shimano.com/#/spec, and compatibility charts here: https://productinfo.shimano.com/#/com/.
Note there is a link to archive docs in the top right of those pages if you want to research older products.
You'll need a derailleur that can accomodate a 53 tooth ring, obviously; but the major compatibility issue isn't with the crank, it's with the shifter. You can figure out what shifter you have use the compatibility charts to find a compatible derailleur.