Key Fob Not Detected & Door Ajar When Turning

2010 Prius, ~ 175k miles

Have been having the following issues which I think are unrelated:

1) When driving and making a left turn, unless it's an extremely slow a gentle turn the dash beeps, I get the caution triangle flashing on the left hand side of the cluster and it says both Key not detected, it turns on the cabin light as it also shows the signal for door ajar and then this resolves. It lasts a few seconds of the cabin light on, and the beeping subsides a few seconds. The flashing triangle resolves after maybe 30s-a minutes. This issue started several months back, it would only happen if I made a particularly aggressive left turn but now it's gotten much more sensitive.

I haven't been left stranded yet, but would like to know if anyone else has dealt with this? My guess is that some connection is loose and needs to be secured? Where to even start looking I have no clue

2) I was getting a low fob battery message so I swapped my fob battery. Since swapping the fob battery maybe one in 5 start ups I get the message on dash "Depress Brake Pedal, Touch Power Switch with Key" -- the rest of the time it works fine. I have also noticed, the fob is not as reliable for locking/unlocking though I am not getting any low fob battery messages.

I'm not sure if they're related issues.

Any help would be much appreciated it!