No, HA did not have a negative value.
In my examples, HA turns positive before reaching the meridian. This is my point. Please take a look at the figures.

Please, excuse my insistence, but either I am missing something very obvious or I see in the images that HA is positive many seconds before reaching the meridian.

Do you ever see HA reach zero? I mean, either further east of possibly at the meridian? The first would mean that the meridian line (or possibly the whole sky) is drawn incorrectly. The second would mean that HA always incorrectly is presented as a positive number.

Yes, HA reach zero before arriving at the meridian. Before that, HA is negative. The star crosses the meridian several seconds later, counting HA correctly but with that time offset.
I also though about a drawing problem in the local meridian line...

Just for verification - you take the meridian line drawn by KStars as 'reference' that defines the true meridian, yes? Could also be the mount is right and the line is drawn wrong.....

Yes. When I say ‘meridian’ I mean the blue line drawn by KStars.
HA is not read from a real telescope, everything on the profile are simulators except for the GPS.
In the second example it was just the KStars planetarium, no INDI running.
How could I check whether the meridian line is well drawn or not ?

If you are using all simulators then I have also noticed some odd behaviors with meridian flips and the mount/telescope simulator. I suspect there is a bug in the simulator, but I haven't had a chance to try to run it down.

Putting that aside, I have found that testing flips with the simulator to be misleading at best, There is usually a group of settings that are very specific to the mount that come into play in getting flips to work. As an example, my Losmandy G-11 with a Gemini II will not flip at all with the default settings I have to play with east/west limits and goto safety limits as well as ekos settings to get reliable flips.

So when I want to test meridian flips I use the real mount up indoors and use that instead of the simulators. That way I have confidence that come 0200 in the morning when I'm asleep, the mount will flip.

J.