I would recommend using Obtainium[1] over F-Droid.
Obtainum downloads APKs directly from the repository's releases page, for example the GitHub releases page.
Why not use F-Droid?
"Due to their process of building apps, apps in the official F-Droid repository often fall behind on updates. F-Droid maintainers also reuse package IDs while signing apps with their own keys, which is not ideal as it gives the F-Droid team ultimate trust. Additionally, the requirements for an app to be included in the official F-Droid repo are less strict than other app stores like Google Play, meaning that F-Droid tends to host a lot more apps which are older, unmaintained, or otherwise no longer meet modern security standards."[2]
Do keep in mind the prior part that explains why they reuse package IDs and use signing keys that way; F-Droid aims for reproducible builds[0]. They also to my knowledge do respect developers that want a different build ID/package title to be used compared to the "official" version. The F-Droid version of Island for example is called Insular specifically to avoid this issue.
PrivacyGuides' motivations here are really aimed for a specific type of user (and I'll note that it's slightly odd for them to place so much faith in a point of origin that's historically been the easiest to compromise: the upstream developer usually is the easiest target, particularly on otherwise dormant software); the tradeoff F-Droid does might be more worthwhile for most people in that they act more like a linux distro maintainer, so there's a second set of eyes to prevent any shenanigans from being afoot on the upstream.
You can as I understand it run their actual servers rather easily (provided you have the computer space to do so)[1], so solving that is pretty easy, should you feel inclined to do so.
Obtainum downloads APKs directly from the repository's releases page, for example the GitHub releases page.
Why not use F-Droid? "Due to their process of building apps, apps in the official F-Droid repository often fall behind on updates. F-Droid maintainers also reuse package IDs while signing apps with their own keys, which is not ideal as it gives the F-Droid team ultimate trust. Additionally, the requirements for an app to be included in the official F-Droid repo are less strict than other app stores like Google Play, meaning that F-Droid tends to host a lot more apps which are older, unmaintained, or otherwise no longer meet modern security standards."[2]
[1]: https://github.com/ImranR98/Obtainium#readme [2]: https://www.privacyguides.org/en/android/#f-droid