Is the battery cycle count stored on the battery or the device?
It seems the issue is that when the battery is replaced, most mom and pop places don’t have the skill or equipment to go in the “root” to reset the counter. It’s akin to not resetting the change oil light on your car. The issue is that some cars use oil life to make other decisions on engine operation, so without resetting the light, performance isn’t fully restored because the computer thinks it’s still old oil and making its decisions based on that. Your battery life, auto shutdown, and battery life remaining display are kind of the same. I bet your phone goes to zero faster than you expect and shuts off, but after leaving it off for a while, you can cut it back on and it’ll show 20-30% or more battery. If so, the thing to do is to keep draining the battery without plugging it in, until after sitting the phone doesn’t even have the juice to try to start, then charge it up to 100, preferably on regular vs fast charge. The life monitor will adjust to the new high and low, and you should have better battery life performance. What’s happened is your phone is basing the full charge and dead capacity off your old battery still, and this process should force it to adapt to your new one.