My CPU is at over 5GHz, 1% load and 70C at the moment. That's in a "power-saving mode".

If nothing would be wrong, it'd be at something like 1.5GHz with most of the cores unpowered.

Something is wrong with power governor then. I have an opposite experience, was able to tune Linux on a Core Ultra 155H laptop so it works longer than Windows one. Needed to use kernel 6.11+ and TLP [0] with pretty aggressive energy saving settings. Also played a bit with Intel LPMD [1] but did not notice much improvement.

[0] https://github.com/linrunner/TLP

[1] https://github.com/intel/intel-lpmd

What is the laptop, and what's it doing?

What p-state driver are you using?