I want to add a racial trait that adds the cantrip 'friends' for a homebrew race, but the spell list to add it is missing it? If I just scroll down alphabetically it isn't there, and if I type to search the only options that are pulling up are 'animal friendship' and 'fast friends', neither of which is what I'm interested in.

You can only attach spells you have purchased access to or free spells to your homebrews. Friends is not a free access spell, so the only way you can add it to your homebrew is if you either purchase the PHB, or at least purchase that spell from this website.

I do not own it myself, however what I was trying to homebrew was for a campaign I am dming for, in which I can access the cantrip because one of the players does own it and is sharing it. Being able to access it in every capacity except this seems really dumb.

Your player can homebrew it, or you can purchase the spell for $2. It is what it is. I don’t make the rules.

Quote from IamSposta >>

Your player can homebrew it, or you can purchase the spell for $2. It is what it is. I don’t make the rules.

 No one in the DDB staff make these rules either. Going to have to bring it up with WotC sales/marketing team.