Good Analysis!
A few points. The fan behavior on the Framework 13 Ryzen is driven by an external thermal sensor which takes some time to respond versus the CPU. This is partially by design, as having the fan respond instantly to the CPU is not an ergonomic tradeoff that many people will want to make. The CPU temperature can go from 40->90+C->40C in a second, having the fan respond so quickly would be unpleasant to listen to.
There are several factors we take into the thermal design of the system including the fan responsiveness, the thermal mass of the heatpipe and spreader, and the acoustic behavior.
We further improved the the fan behavior on the Framework 16 by introducing a virtual thermal sensor algorithm, which is essentially a low pass FIR filter fed by the die temperature. This allows us to tune the fan responsiveness by adjusting the filter parameters. This allows us to emulate placing a physical thermal sensor at different distances to the APU, without having to layout a new PCB. Which solved a similar issue on the Framework 16 APU and GPU.
We are investigating back-porting this new technology to the Ryzen 13 platform.