What it needs
The EP-133 runs at 46.875 kHz in 16 bit, mono or stereo. The rate is genuinely that, and it is the one number on this site most likely to be read as a mistake.
The internal signal chain is 32 bit, so the 16 bit figure describes what you hand over rather than what happens after that.
Format WAV Sample rate 46.875 kHz Bit depth 16 bit Channels Mono or stereo
Getting the files there
Samples go on over USB using Teenage Engineering's sample tool. The device presents itself for transfer and the tool handles the rest.
Prepared folder on disk
Kick 01.wav 46.875 kHz 16 bit
Snare 03.wav 46.875 kHz 16 bit
-> Teenage Engineering sample tool, over USB
-> EP-133 K.O. II
Doing it in Sample Miner
Export Options has a Hardware target dropdown. Selecting EP-133 K.O. II sets WAV at 46.875 kHz and 16 bit, leaves the channel count alone and clears the sampler format.
No general purpose converter offers 46.875 kHz in a menu, which is why this is a preset rather than something to dial in.
Why 44.1 is the wrong default
Handing the EP-133 a 44.1 kHz file means it resamples to its own rate on the way in. The result is fine and the process is invisible, and you have still let a conversion happen that you did not pick.
Matching the native rate on the desktop removes that step. It is a small thing per sample and it compounds across a kit.
The limits
Onboard storage is fixed and there is no card to expand it. What goes on the device is a selection rather than a library, so the choosing is the work.
The EP-133 maps samples to pads rather than to keys, so a chromatic multisample does not arrive as a playable instrument.
Sources
Specification confirmed against Teenage Engineering documentation.
Other devices: Digitakt, SP-404 MKII, Model:Samples, M8, Lofi-12 XT.
What the files themselves contain is in the format reference, and the words each sampler uses are in the glossary.
To check a file you already have, drop it into the file inspector. It runs in the browser and uploads nothing.