Switch is a handheld, because:
TV play is not a defining feature of either home console or handheld.
The clockspeed changes are artificial and have no hardware-related reasons, only personal preferences. (The switch runs just fine at ~max clocks even if undocked).
What people use it for doesnt matter, otherwise I could start (mis)using people as punching bags and get away from it, as that "person" will now be considered an
"item itended to be punched" not a human.
A hybrid is defined as something that merges 2 or more functionalities, which the individual items arent capable off. This is not the case with switch, as the entire hardware needed to perform its intended task (play games) is used in either setup.
A proper hybrid external hardware to allow for things the other set of hardware is (physically) not capable of. E.g.: a GTX 4090 inside the dock which is used instead of the GPU in the SoC when docked.
A suprisingly constant feature of home consoles is that you can theoretically swap everything in the system without altering its use case.
You could for example add so much more hardware to a home console that it becomes a cubic metre big, it wouldnt affect how you use it. Try the same with a handheld and it wont work anymore. Yes I know this is a theoretical example.
So.. neither the PSP nor the Switch are home consoles. The switch merely offers features which naturally integrate into a handheld, which arent necessarily required.
After all, there are HH defining features, HC defining features and neutral elements.