I use Ventoy for that. I followed the instructions for installing Ventoy, then simply copied memtest86-usb.img from the downloaded memtest86-usb.zip onto the partition created by install of Ventoy.
While the documentation of Ventoy seems unclear for things other than .iso files, it works fine for this .img file.
I expect the same .img file could be put almost anywhere and then loaded by a menuentry from grub.
Maybe it won’t work for secure boot, but it certainly works for EFI without secure boot.
If its setup doesn’t work, it isn’t hard to manually create the menuentry you need.
For the non USB setup, creating the menuentry and copying the img file is all that is needed for “setup”.