The 4A splitter won’t fry it. I’m using this exact one with my sensecaps. Think of it like a PC Power supply, your computer probably isn’t using all of that 1000w 80+ Titanium PSU, but it could.
https://www.amazon.com/dp/B07YB1JF2G/ref=cm_sw_r_awdo_navT_a_8PH60V39NW25E8PMQ7GM
There is also a Raspberry Pi4 in the product images. The same guts that are in your hotspot.
You also want a quality injector.
https://www.amazon.com/dp/B08LZZRX5N/ref=cm_sw_r_awdo_navT_a_G2WY7AJCXKGZ5Y7KZCX9
https://www.amazon.com/TL-PoE160S-Injector-Supplies-Wall-Mount-Certified/dp/B08LZZRX5N/
https://www.amazon.com/TRENDnet-Ethernet-Injector-Distances-TPE-115GI/dp/B00BK4W8TQ/
The Ubiquiti PoE injector isn't going to communicate with your UniFi controller.
It's not going to show up in your Network Map with a sexy power consumption graph.
A PoE injector won't have an IP Address. It doesn't have a GUI to configure.
It's going to boot up and it's little "I am powered on" LED is going to glow, and that's it.
There is nothing special or magical about the Ubiquiti branded injector.
So long as you purchase an injector that is compatible with either 802.3at or the 802.3bt standards, it will power that Access Point.
If you want a white one, find a white one on Amazon.
But if you think about it, you're probably going to mount it out of sight, so IMO the color of the injector doesn't matter.
If you pick one that doesn't have some kind of a mounting bracket, you're going to have to use gravity, sticky-velcro or a similar solution to keep it in place where you put it.
But I acknowledge OCD is a thing, so you do you.
It doesn't have to be Aruba. Any midspan 3at compatible injector will work fine, like this one. https://www.amazon.com/dp/B08LZZRX5N
https://www.amazon.com/TL-PoE160S-Injector-Supplies-Wall-Mount-Certified/dp/B08LZZRX5N/
Admittedly, I'd rather avoid any Chinese "branded" stuff even though this is just power delivery (speaking as someone that is part Chinese too....)
But I acknowledge OCD is a thing, so you do you.
Don't have a diagnosis, but can confirm I suffer from this severely in my own home.
That said, it's not for me and we don't care about the color as it sits in a room nobody ever sees. Just wanting the official one to avoid any issues as taking time to diagnose is time away from more important things. The official POE+ injector says it has remote reset. If it doesn't show up in any GUI, how do you remote reset it?