HOWTO: build install a DKMS module?

Yes and in addition this sentence from @lwfinger is related: “Beginning on November 4, 2019, I will NO LONGER support people that have downloaded the source as a zip file.” Which means that git clone https://github.com/lwfinger/rtl8188eu.git is better place to start.

And even this post: Purism on IBM T420 should work there for you, as optional one, confirming that the “r8188eu” driver (inside of firmware-realtek package) is now, I think, integrated, thanks to lwfinger, for … as here linked phoronix.com article describes.

EDIT: https://packages.debian.org/bullseye/firmware-realtek.