The microsecond level time measurement function timer_u32() is available in
https://github.com/OliviliK/ESP32_timer_u32
The example is timing of fibonacci function up to F92. The function takes 0.3 - 9.0 microseconds to execute. The timer_u32 uses two methods (FRC and TG0_LAC) on ESP32 and one method (SYSTIMER) on ESP32-S2.
In the original post the code was demonstrating the different results for different data types used in fibonacci function. The Github code demonstrates that the SYSTIMER or ESP32-S2 has very different speed profile than ESP32 with FRC. The FRC numbers seem to be more believable.
Perhaps there will be some follow up to explain the unexpected results. The good thing is that now I have not "found" a serious problem in ESP32 hardware.