scrampker The Pixel 7 Pro has the exact same SoC as the Pixel Fold, they both have the Tensor G2, and they both have 12GB of RAM. The Pixel 6 Pro also shares 12GB RAM with the other two above devices, and carries an original Tensor SoC, which is very similar to the Tensor G2. .
It only differs in that the mid cores were upgraded to a slightly more modern (but not completely modern) core by changing out the 2 Arm Cortex-A76 cores for Cortex-A78 cores. The rest of the chip remained the same.
Both chips were known for heating up quickly, and when I had my Pixel 7 Pro I ran it rooted with a locked bootloader and verified boot for months. I ran a kernel manager that allowed me to examine and adjust the governors and clock speeds on the different cores, but I couldn't override the thermal throttling. As soon as the prime cores (2X Cortex-X1) powered up to max, they only could hold that speed for less than 10 seconds before the whole chip, all three sets of cores throttled down! They were programmed with the default SchedPixel govenor, a custom one Google made, to almost never go up to their full speed however. They usually would boost up when system was under heavy load, like >70% for periods of <2-3 seconds then go back down to 500mhz to rest. Only when doing really heavy loads did they get going and that resulted in the whole chip throttling!
Really I'm not surprised that both your devices, having those SoC's, your having issues. However the issue with your apps closing so fast in the background is a new one to me... It sounds like in Developer Options, "Suspend execution for cached apps" may be enabled, but I'm not sure. Maybe try setting this to disabled?
I think you need to swipe your notification screen down twice, to get to quick settings and in the right bottom part it will show you how many apps are active in the background. My Pixel 8 Pro runs great at between 4 and 8 even at a time. No problems like you are reporting at all! My zRAM is mostly full but I always have around 2GB of RAM free, and yours should as well unless you have a lot of apps in the background and running! Check that place in the quick settings screen, and when you click on the number you get a screen where you cab stop those apps too.
Be glad you didn't geyvan 8GB model like a regular Pixel, I don't think those would deal with backgrounding apps well...