scrampker if you had a Pixel 8 Pro it would be a much smoother experience, I can tell you from the months I've had with mine!
Does it thermal throttle? Well yeah, all smartphone chips thermal throttle. Especially that beats they can the Snapdragon 8 G3! That one gives amazing performance for a but then it's a crazy swing down, almost to the Pixel 8's performance, then up, then down again from the graphs I've seen! The same graphs didn't have any G2 Tensor devices in then, but the Pixel 8 Pro took a while to start throttling, then it did so slowly and consistently, kind of like the iPhone chips just not with their level of performance.
Running my kernel manager, I've seen the G3 in the 8 Pro throttle down, but back up quickly. It starts to throttle at a lower temp than the G2 in the 7 Pro did, by almost 10 degrees! Probably to not get so hot, which was a complaint of the predecessor. But it pulls out of the throttling quickly too once it has a short break. Also the cores deliver better performance at low clock speeds.
Bear in mind, the Pixel 8 and the 8 Pro perform differently, with the 8 Pro being a much better performer! Same was true between the 6 & 7 regular and Pro models. (500 Geekbench points) I think its the larger chassis that is a heatsink for the chips, and then larger surface for radiating the heat. I have an OtterBox Defender for my phone when I'm out, and its a huge insulator, so I peel it off at home before doing more intensive stuff with the phone.
As to the running app button, if you pull the notification shade down twice to get to all the quick setting buttons, at the bottom there will either be a lock and message saying you are connected to a VPN, and if you click on it you go to VPN settings. If you are not on a VPN that same large oval at the bottom will pop up the list of running apps in the background! If on a VPN, then you will find a small circle with a number in it directly to the right if that large oval. Click on that.
Didn't think to add this before, make sure your in the owner profile! I always am.
I also think it is good practice to pair down the number of apps running in the background. At the end of the day, its still a phone!
You can also check for running apps in Developer Options. Right near the top there will be, right under OEM unlocking, Running Services. It will show the actually running processes, but click the three dots in the upper right and you get the second screen with "cached processes" and there you'll also see the true value for your remaining RAM!