I noticed my MBP 16 would get laggy big time after some time of use but I mainly noticed this when I installed Big Sur and BetterTouchTool. I was suspecting its the Touch Bar software I put in causing this so what you said here sounds like what I suspected. I guess no more BetterTouchTool and probably got to run this on the 5300. The primary reason for me to have Touch Bar over physical buttons in the BetterTouchTool and if that is crap on this Mac than I dont know is Touch Bar is all that fancy since I really liked to have the DOCK on the Touch Bar.That lag is caused by the TouchBar and the T2. The system waits for the Touchbar to change what's on the (Touchbar) screen and the T2 (which actually drives the Touchbar) also handles all input.
Depending on applications and system load, the lag is more or less noticeable but you cannot completely fix it because of the way the system is built.
I also had some micro-freezes on my system when on the iGPU. First I got my machine exchanged like 6 times. All had the same issue. Finally, I got rid of that by installing the Big Sur beta back then when it was released (which updated the T2 firmware). It was completely solved even when booting Catalina. Now on Big Sur release, the freezing didn't came back yet.
But the iGPU still has some general lagginess. It's simply because the UHD630 is pretty weak and cannot properly drive the heavy UI system of macOS at the high resolution.
To fix that you have to do one or more of the following
a) Reduce (render) resolution
b) Reduce complexity of the window and UI system (will never happen)
c) Increase performance of the iGPU (not possible)
d) More aggressive clock scaling on the iGPU (possible by Apple). This increase power consumption and will only reduce lagginess to some degree.
Alternative: Run on the AMD GPU all the time and say goodbye to your battery time.