In case it is of interest to developers, I will make notes on the problem step-by-step on a family member’s phone. It is a Samsung Galaxy A52 running Android 13.
It has F-Droid 1.16.3. It is configured for Updates Over Wi-Fi all the way to the right and Over data halfway (which I am leaving as is, as wi-fi is preferred and this would not explain why it does not show an update is available). Auto update interval is daily, Show available updates is ON. (These are probably default settings.) There is no badge on the F-Droid icon showing any update is available, even though there should be updates for F-Droid and Aurora Store. In fact, Aurora Store hangs when I try to start it, probably because it is the old version, 4.2.3.
In F-Droid, as someone suggested, I went to the Updates screen and pulled down to refresh updates. It says “Updating repositories” and then: “Congratulations! Your apps are up to date.” This is what I am trying to get across: F-Droid is not telling us we need to update F-Droid and Aurora Store (and maybe other apps). The last Android update was installed 4 days ago, and the phone was restarted a day or 2 ago.
One thing is different on this phone compared to my phone. On my phone, even when I updated F-Droid to 1.7.0 (but without first uninstalling 1.16.3), when I searched for Aurora Store, it showed only the old version, 4.2.3, as if it were current. On my family member’s phone, when I search in F-Droid 1.16.3 for Aurora Store, it does show the new version, 4.2.5, and it provides an opportunity to update. AND when I search for F-Droid, in the list of search results, it shows F-Droid 1.6.3 with no download button, but when I tap on F-Droid, it says Updated 2 months ago, and shows an update button.
I tap on Update, and F-Droid updates itself to 1.17.0. There is no badge showing the number of updates on the F-Droid icon on the home screen, but when I open F-Droid, at the bottom of the screen there is a 5 next to the Updates icon (a bell) and now it shows five apps, including Aurora Store, that have updates available.
It would be nice if there were a quick and easy way to check on the latest version, but I have not found it. When I go to F-Droid.org, the latest version number is not on the home page. I can tap the download button, but the version number is still not displayed. I could not find the current version number anywhere on the home page or the pages easily accessed from the home page. Somehow, I did find this page which has information on the current version:
I will bookmark it and share it with the rest of my family, so we can easily check if we have the current version in the future.
(Once F-Droid and Aurora Store had been updated to current versions, those apps were each able to update various other apps which they manage.)
So, at least for the phones in my family, we do not receive notifications of F-Droid updates, so an email list would be great. I would guess there are at least a few others who also do not get automatic updates of F-Droid through the F-Droid app.