@jeanjballard
With a USB cable there are not just plus and minus power wires, but also data communication wires. I assume the phone is trying to talk to the charger but can't for some reason, giving you the silly "broken cable" message. In most cases it's probably true; the constant flexing of the cable does tend to break wires inside over time, but obviously not every charger you have has broken wires.
In that case we have to assume it's something inside the phone not letting it talk to the charger. The first and most obvious choice is the charging port itself. It's susceptible to wear from being plugged and unplugged daily, it can get dirt and lint lodged inside preventing a connection, and the pins inside can get bent and broken.
So if you've already cleaned the port and checked it for damaged pins, then the first step in fixing the problem is to replace the charging port. On Samsung phones its located on a small daughter card at the bottom of the phone that inexpensive and relatively easy to replace, as phone repairs go. I didn't find any iFixit-style written guides to that repair for you, but I did go through a couple of YouTube videos till I found one that looks complete and instructive.
Samsung Galaxy A32 5G Charging Port Replacement - No Soldering Needed - YouTube
If replacing the charging port doesn't fix the issue, you could try replacing the flex cable that connects the daughter card to the motherboard. If neither one helps, then it would have to be something wrong with the motherboard, which would require specialized expertise and equipment to repair.
Hopefully it's just the charging port and that gets your phone up and running like new again!
And as you work, take lots of pictures and once you're done you can use them to create your very own iFixit guide to charging port replacement on your Samsung Galaxy A32 5G. It's easy, fun, and will earn you the gratitude of the repair community.
Create a new Guide - iFixit