What internal electronics do Spike Prime and Mindstorms Robot Inventor use? What electronics live inside the SPIKE Prime hub? How powerful is the hardware?
If we open the hub we can take a look at the main PCB inside. There's just one PCB in addition to a small speaker and the replaceable lithium ion battery. Here's the top of the PCB:

And the bottom:

We see that the main CPU is an STM32F413. It includes 1M of flash and 320k of RAM and the ARM Cortex M4 core can be clocked up to 100MHz.
In addition to the 1M of embedded flash, there's a Winbond W25Q256JV providing an additional 32MB for program and data storage.
Bluetooth connectivity is provided by the TI CC2564C.
The 25 LED grid is driven by a TI TLC5955 (48 channel PWM LED driver). This part also drives the other 4 surface mount LEDs on the board.
The 6 motor outputs are driven by a trio of LB1836 dual motor drivers.
There's also an MPS 2639A to manage the lithium ion battery.
There are many other supporting components on the board, but that covers the majority of it.
Overall, this is similar in architecture (ARM-based, identical output drivers, etc) to the other Powered Up hubs. It is significantly more powerful in terms of horsepower and storage thanks to the 32MB flash chip and higher clock frequency (100MHz here vs 48MHz for Boost for example).