2013 Toyota Prius rough starts and P0517

Hi! I have a 2013 Toyota Prius with 262k miles. At around 202k miles we had a head gasket repair done. It's had 3 rough starts recently that remind me of when it has a bad head gasket.

Coolant level is fine oil level is fine and oil looks fine. (Just changed oil 2k miles ago) But... admittedly I never kept up on cleaning the EGR system. Even though it's having the rough starts with misfire there isn't a check engine light. I thought I'd check for codes just in case and got P0517 bad battery temperature sensor? I'm assuming that this is a whole separate issue and not related. I've had the hybrid battery replaced in the past and checking with the installer to make sure it won't void the warranty if I replace the sensor. Also tested the hybrid battery since I was playing around with the OBD2 scanner and Dr prius said "poor balance block #4".

So do you guys think the issues are unrelated? And do you think it's got another blown head gasket? Would cleaning the EGR system this late in the game prevent another blown head gasket if its not blown already?

I appreciate any advice! Thank you!