Let me report some encouraging results:

I built the v-curve manually. I started in the acual focus position. At iso 800 I got an HFR of 3.9 for the optimal focus. I moved away from the optimal focus position in far3 steps, until I could see a really substancial increase of HFR. One far3 step did not change anything. The second gave a small change. The third step shifted HFR to 11.28. Since I new I had moved in far-direction I started moving inwards in near2 steps. Over the first 8 steps HFR did hardly vary. Then HFR started to decrease almost linearly until it reached a value of 3.91. Then the HFR started to increase almost linearly. I got a beautiful v-curve with a clearly visible minimum.

At HFR 12.36 I turned the direction of movement again and moved outwards again in far2 steps. Again over 8 steps nothing happened and then HFR decreased to the minimum and increased again.

At the next turnaround I tried 1 near3 before moving inward in near2 steps. Now I only had 4 backlash steps before HFR began to decrease.

Continuing this type of systematic variation I found that the change of direction should be done by two big steps in the oposite direction. This has the same effect as a instantaneous turnaround (no backlash) and about 3 steps of medium size in the oposite direction.

One safe way to reach the optimal focus position might therefore be to build the v-curve moving in equidistant steps in one direction. After the minimal HFR has been passed, one should continue at least 3 more medium steps into the same direction. Then make a turnaround with two big steps in the oposite direction and return to the minimal HFR in medium (or small?) steps.

I attach some screenshots and an excel sheet with the data I took. ...no, it won‘t let me attach the excel sheet.

One issue is, that the backlash is probably specific for different lense types.

Here comes the zipped excel.

Maybe the existing algorithm could be made working correctly if we introduce a backlash on every turnaraound, which might be adjustable. For my tamron the backlash would be 8 medium steps.

Today my lense does not move at all no matter what I do. It won't focus neither with or without LiveView activated. I'm unsure whether or not this is a user error.

Try to enable view finder mode in the action panel of the indi dirver and select an item from the far3...near3 drop down menu (no matter which item you choose). This worked for me.

Nope, sorry. Have there been any changes to the driver lately? It did work recently, albeit moving the mirror 80x up and down. No click-clack today at all.

I didn‘t upgrade today ...

Then don't do it.

I tried gphoto2 --shell commands and these do work. So my cam is OK. Are there any other camera settings that might prevent focusing from doing its job? Who knows, maybe I have changed some inadvertently.

Now focusing via Indi panel works again but the autofocus routine in Ekos won't move the lense at all. I can hear the mirror does not go up (other than for taking pictures) so it appears to me LiveView mode isn't activated at any time. Lots of pictures are being taken but they are all the same.

Awesome data Christian! Ok, so I might either have to adjust t he Ekos autofocus algorithm, or make one special for DSLRs. I need to examine the data and see how it can accommodate that.

Will investigate this more once I get the artificial star.

Herrhausen, I would like to help, but I am afraid I don‘t know any new advice. When I experienced the autofocus routine wouldn‘t move the lense, I could solve this by manually enableing the view finder mode in indi AND select an arbitrary focus move from the drop down menu on the same panel.
I noticed that after a live view window is closed, view finder mode is being disabled. In the inidi panel it remains checked as enabled, though. Then I had to re-enable viewfinder mode by unchecking and rechecking it in the indi panel.