Hello, I've helped a couple of people through problems like this before, as far as stripping down the hybrid battery into it's individual cells and load testing them before replacing any bad ones and then balancing the cells ready to go again, although that is beyond the scope of this message thread and depends on how technical you are also.
The code P3000 code logged in the main ecu, is essentially an advisory code that there are codes in the hv ecu that need reading.
The HV ecu has given you C1259 which is a malfunction to do with the regenerative braking battery charging and the C1310 code points to the skid control side of the HV ecu during regenerative braking.
Given the above and your description, paying attention to the non charging and fast discharging of it, the HV battery pack needs removal, testing and repair.
The only exception I have ever heard of is as below, this is a cut and paste from another website.
"Ultimately the problem was simply a CORRODED CONNECTOR in the electrical wiring harness connector plug. In the right rear part of the car near the 12V battery and blower motor. Some members of this thread had suggested loose or corroded connections as the culprit and they were absolutely correct! Thanks! This is a relatively common problem and can throw codes that have absolutely nothing to do with item referred to in the code (like VSC). So when you get these codes, don't always assume the main battery is bad (even tho the codes indicate that) and spend the extra time tracing and inspecting/testing all the wires and connectors that you can reach when you are making these repairs. In my case it was ultimately simply a $5 repair. Since I experienced this, I have read numerous cases of others having the exact same corrosion issue in the same place. I hope this helps others in a similar situation! "
Has to be worth a look and checking for the plugs as the HV battery repair is long winded to say the least.