I use two methods:
I originally send them out as links (to files in my Amazon S3 account) in the text portion of an image post. The image shows a thumbnail of the wallpaper, and the link lets patrons download the file.
For content I’m happy to leave up for any patron to discover (and that I think will be unlikely to be hotlinked elsewhere), I just keep the links in the post. The “panel wallpapers”—based on the winning panels from my pages that patrons chose—fall into that category.
I do have some things up for a limited time, however, like any 18+ content. In the current month, those pin-ups are available to my $5+ patrons, and I post them as links as usual. But after that, the links get removed and the files go to a “Digital Library” where only my $10+ patrons get access ($10+ gets access to every pin-up I’ve ever posted, $25+ get access to high-res versions of those pin-ups.)
I use the Patreon integration with itch.io for those download libraries. Itch.io is free, they are cool with 18+ content, and they allow granular Patreon access, so I can have separate libraries for my $10+ and $25+ patrons.