I'd reach out to the Inkbird folks on their website. I was just looking up the specs of the controller, and they've got a little floating help bubble and listed a bunch of people currently online you can chat with.
But assuming you're looking for some opinions... My guess is the commercial grade freezer draws more current than the controller can handle. Looking at the specs for the itc-1000 (as well as the itc-308 that I use on my 10 cu ft keezer, and is super common/popular in the homebrew world), it's rated for 10 Amps.
Your freezer label says 4.0 Amps, but that is probably a standard operating load. Reading some rando-website, it says a rule of thumb is that start-up current is 2-3x operating current. So that would say maybe you're getting spikes of up to 12 Amps to get it going, which is more than your 10 Amp controller could do. Plus, with age, maybe that number could be higher.
As a sanity check, I looked at a run-of-the-mill Insignia 10 cu ft chest freezer from Best Buy uses 1.4A. So your ice cream freezer is pretty powerful. So that's why myself (and probably lots of others) can operate their keezer with an itc-308 or itc-1000 and not have the kind of start-up issues you're seeing.