Glasshopperus

Perfect! Now I may be able to help a little.
You could  try Axpert King Rack Mounted firmware version 75.08. They may have fixed the PV issue by then.
 

Could it maybe be warning 69 and not error 61?
Kings used to show warning 69 on some firmware versions if the battery is fully charged and the inverter still tries to push charge into it.
Are the batteries properly chained and configured? It is very strange that they show different voltages. There are some dip-switches that you need to configure to set master and slave batteries. Dip-4 off for master and dip-3 off for slave. I cannot see it clearly on the video, but they all seem to be on for both batteries.
It is also necessary to configure communications on the battery to match the Axpert King protocol as described in the user manual.

@Coulomb is correct, error 61 is BMS comms error and you will only get it if you are on PYL, Lib or Lic settings, you won't get it when set to USE battery type and set the voltages. That way you can at least know if it is the BMS comms causing the issue or not.
It might be that the new comms board doesn't give error 61 because it connects to the BMS, but there might be an error in the protocol implementation when the battery reaches 100% causing your issue.

Hello, thanks to everyone who replied. It turns out my 48v Axpert King rack 5kw was one of the first released so its communication card could only talk with PYLONTECK stackable lithium. The newer models have a different communication board that can speak to any Lithium. So €108 later they have switch my communication board and it all worked. (For a short time I will post the update later 🤦‍♂️🤣) 

There definitely seems to be something strange going on with the BMS comms... the inverter is trying to push charge into the batteries even though they are both at 100% SOC. If comms was working, one would expect the inverter to go to float and not keep trying to charge. Have you tried removing the comms cables and running the batteries in USEr mode on the inverter? If that alleviates the problem then you know it is definitely a communication issue.

There is something strange with that pair of battery modules. At one point in the video, one was at 54.x V and the other at 55.x volts. Also, they don't share the current, one is always showing zero.
Is one of them showing a fault LED? Maybe cycle the power on that battery module?
What is your main (U1) firmware version? Some models, I think early Kings, possibly including the rack mounted versions, had a firmware fault where if the BMS told the inverter to stop charging, the panels would be shut off (forgetting that a big job of panels is to support the load). This was fixed in later firmwares.

Hello, thanks to everyone who replied. It turns out my 48v Axpert King rack 5kw was one of the first released so its communication card could only talk with PYLONTECK stackable lithium. The newer models have a different communication board that can speak to any Lithium. So €108 later they have switch my communication board and it all worked. (For a short time I will post the update later 🤦‍♂️🤣) 

2 point2 How are your panels connected-like in per series string and then number of parallel strings? 
Normally one would save the videos where one can upload like YouTube and then just supply the links. 
Some sites allow you to host the videos and then link it to the videos. 

Is one end marked battery and the other inverter? Maybe you used the special cable between battery modules? 
You also need to choose the correct battery type for your battery. Does your battery documentation mention compatibility with Axpert inverters? 

Not to say the cables are faulty, but the standard cables are different to that blue one. If you have tried swapping the ends around (what is in the battery goes to Inverter) and it is still not working, them maybe try order the original cables. They look like the black ones with the yellow tags. (From the battery manufacturer)
Also, check you battery DIP switch settings. (Again from battery manufacturer). Different for different batteries. And you set the Dip Switches while battery is OFF. They don't always catch the first time round, especially when system is on.
 
 

Good evening @Glasshopperus
The battery communications cable (blue cable that is connected to the CAN / RS485 connector on the battery) must be connected to the BMS connector on the inverter not to the RS232 connector on the inverter.
Make sure that the battery communications cable has the correct connector pin-out on both connectors otherwise the communications between the BMS and the inverter will not work.
If the battery communications between the inverter and the battery cannot be established then the inverter must be set to USE for program 5 and the voltages must be set for program 26, 27 and 29.
Kind Regards
GerhardK83

I would use what the battery manual suggests as they will know how their addressing system works on the BMS. Your battery seems a little different as it is flipped from what is usually used.

I will start by setting the master based on the battery manufacturers settings. Some master has #3 on and others off. Then you turn on master battery. The above for a King and Growatt for the same battery will be #2 on on the madder and all the slave have all Dips in the off position. 
As you indicate the inverter manual might indicate for the Pylon profile. 
If you use a non Pylon battery I take it the positions will be different. 
I stand to be corrected on the above.