Good news to report
I opened it up and measured the blue battery pack inside the controller.
Since there was no writing on the original battery I referenced the Nintendo Brand battery pack for the details I should be looking for.
I found a battery of similar size on Amazon. I made sure to double check the connector clip and wiring arrangement matched the blue battery I was replacing. I was unable to find one rated at 1300mAh that had dimensions that would safely fit inside the controller battery cavity. The battery compartment back plate has a curve in it that I feared might not leave enough room to reattach the back plate if I got the taller 1300mAh version. It may have fit just fine but I chose not to risk it. I ended up going with
this battery for $11.99. The 1200mAh I purchased fit comfortably inside despite being 1.3mm greater in height than the blue battery.
The lights on it blinked so I tried to sync it immediately. But the WiiU could not see it. I cleared all paired controllers for the system and then tried plugging it in via a USB cord to sync it. Still no luck. I decided to charge it fully to see if that would make a difference. It did not. A little looking on gbatemp and I
found someone who had the same issue.
They reported that with Tiramisu and Bloopair active their brand new WiiU Pro Controller would not sync. But after rebooting their WiiU without the SD card present (which contained Tiramisu and Bloopair) the controller synced successfully. I tried that and my controller synced like normal. Yay!!!
So all is well and I didn't have to throw this very well built off-brand controller into the trash. Thank you everyone for your help and guidance. I sincerely appreciate it
