So, I have a partial solution by now. I’m still not sure why the solution works and others don’t but anyway I will write it down for the moment as it is.
But first of all, thanks to @Ingo and @DietmarP for their continuous answers.
Since I tried so many things I will try to structure it a little.
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So, from within the contacts App you can click on the 3 dots and choose manage accounts. At least that was the default for me. I could then click on “Add Account” which always opened a windows asking for an e-mail. I suspect as default the idea was an exchange account.
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I entered a account which works with imap. After setting this up I could not choose this one in these settings. Which doesn’t come to much of a surprise from a technical point of view but oh well I tried another one. What I did not try was a Google account.
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Next step was to install an App called DAVdroid which can be used to sync caldav and carddav things. Since my main e-mail account does not support such things I went for a “web.de” account because I suspected they support features in this direction.
Setting up the account was easy and worked out of the box. Understanding the result was not so intuitive. In the end this account gave me a CardDAV and a CalDAV entry. In order for things to work at least the CardDAV entry has to be checked.
To prevent uploading to these servers anything I tried to disable any automatic syncing, within this App. Within the Contacts App and also via the Account Settings of the general settings. Testing showed that this was not successful so I tried to alter the account settings in such a way that at this point things will fail what has proven to be the most save solution.
- With this set up correctly it was now possible to select via the Contacts App Account Manager the DAVdroid Address book account. I exported all my contacts and when importing them again I could choose now the DAVdroid address book and behold, the birthdays are shown again.
Finish.
To me it still not clear how and when exactly I added the correct account and why it was possible. Also the “Account Manager” started from within the Contacts App is different from the one under the general settings, even though they look similar (Which makes sense in the end). I think in the end the trick was to select the DAVdroid CardDAV which I set up, via the system settings Account manager. Because there it was possible to choose this directly (DAVdroid has two entries there, one explicitly has Addressbook in its name). But it is also possible that the system recognizes this automatically and I just didn’t have the CardDAV checked correctly within the DAVdroid App.
What also became quite visible during this extended workout. The calendar App has a similar issue. It is not possible to have a dedicated calendar locally on the phone. At least my first superficial tries strongly indicate that.
To point 1. I actually manged to end up in a state where I didn’t have the setting dots within the Contacts App anymore at one point. This was when I unchecked the CardDAV account within DAVdroid and had an empty address book.
Summary: You need an address book account (e.g. e-mail CardDAV, exchange,…) on your system which is able to sync contacts in order for it to add it within the Contacts App to have the Birthday field. I have not found a stable way to disable the sync functionality so far an invalidated the account credentials after set up (resulting in some error messages sometimes).
Any questions or suggestions, feel free to contact me.