Likely Hybrid Battery Dead - Error Codes

My 2006 Prius started "stuttering" at low speeds first. Not always but when getting going from a full stop, as if it didn't want to kick into gear, or the gas engine had a piston that wasn't firing correct. Sometimes the car would have trouble maintaining speed if going uphill. I noticed the fuel efficiency dropped to around 30 MPG or so also. During the pandemic I wasn't driving the car much. It was driven once a week at best, sometimes less, and not for very long distances.

Finally a few days ago I went to start it up and it went into drive, but gas engine wouldn't kick on. Battery power was able to roll forward maybe 20 feet, that's it. Dash error messages are the brake light is on, even if brake is off. Master warning light (the red triangle with the !), check engine light, and charging system warning light (little battery with - / + symbols)

Turned car off, tried to restart, only went into neutral or park. Wouldn't shift into drive or reverse. I went down a list of troubleshooting, all fuses are good. I checked the 12v battery, It is 8 years old and I found the neg terminal was very corroded. I replaced the 12v battery already. As I would test starting after each troubleshooting attempt, a couple times it would go into drive, but gas engine still wouldn't kick on. Most times wouldn't even go into drive though.

I also found the inverter coolant level was low. I topped it off, and after doing this (I believe just by coincidence) when I started car the gas engine actually came on, and the error lights didn't pop up. But when I turned it off it wouldn't start again, and wouldn't go into drive since. I had it towed to a shop already.

So here is the question. They reported the following error codes:

P300 - Indicates that one or more cylinders are experiencing misfires
C1241 - Low Battery Positive Voltage
C1259 - HV System Regenerative Malfunction
C1310 - Malfunction In HV System
P0A80 - Replace Hybrid Battery Pack

So all this mostly points to my hybrid battery is done. My concern is the P300 code. Could the cylinder misfire be a larger engine issue? The car started having these issues before the battery went out. Could this trouble have been directly related to the hybrid battery dying or is it likely something separate? What are the chances it's just a bad spark plug? I don't want to invest in a new battery for the car if it also has a serious fix expense with the gas engine too.

Finally, the shop wants to replace the drive motor battery fan assembly at the same time as the hybrid battery replacement. It sounded like it wasn't damaged, just something they normally automatically do when replacing they hybrid battery. Is this something that's generally recommended or necessary? I attached a copy of their work estimate. Feedback please.