I have a switch on 4.0 running sx os 2.5.1. Playing skyrim in handheld mode drained the battery in an hour and a half. Is that normal?

Afaik, switch has only 1 clock speed when not docked.It all depends on what clock the console is running for the game. Skyrim requires a high clock to keep up to its *ahem* high optimization so battery can drain even faster than Breath of the Wild.
GPU clock speed can go from 307.2 MHz to 384 MHz while undocked. About 20% of difference. Don't remember if it's game specific locked frequency or dynamic scaled, however.Afaik, switch has only 1 clock speed when not docked.
There’s also a 460.8mhz configuration that isn’t labeled as docked or sdev only on https://switchbrew.org/wiki/PPC_servicesGPU clock speed can go from 307.2 MHz to 384 MHz while undocked. About 20% of difference. Don't remember if it's game specific locked frequency or dynamic scaled, however.