They don't. At least not yet. Which is good. There is no central database to control.
Discussion
"Good thing..." Yes and no. Thus my response/question. The OP had mentioned they "searched" F-Droid.... and only found one app. Without discovery a person that doesn't know the app names for the functionality they seek may never find the available options.
I agree installs should be done via obtainium but something is needed for discovery. I've run across this issue myself when searching for various bitcoin and crypto wallets. Web search alone isn't always enough.