Yeh good questions. Firstly in terms of recording times for the BMPCC 4K, you are really constrained based on codec, framerate & internal SD card or SSD you are recording to; i.e. it will record until the SD card or SSD is filled up. I reference the following if I need to remind myself:

https://cinequipt.com/resources/resources-sidebar/blackmagic-design-pocket-cinema-4k-camera-record-time-chart/

The Studio camera is the same however there is no internal storage & we only record directly to an external SSD. Again, it records until the SSD fills up.

I have not noticed overheating issues on either studio or pocket but I only ever record at most 3 hrs at a time.

In terms of additional features the Studio cameras have over the Pocket: the Studio has a larger screen, tally lights, talkback features, and broadcast quality (NTSC & PAL) i.e. things you expect in a broadcast environment. The Studio Pro has a further set of features such as SDI connections, Ethernet for upscaling to a Blackmagic Studio Converter & two XLR inputs which is great if you want to feed audio in via an XLR mic as the Atem Mini Extreme only has a 3.5mm jack for audio input (removes the requirement of having to setup an audio interface). So you probably just need to see if these extra broadcast features would be utilised in your setup.