..."

I start to suspect there is some kind of "conflict" in the Projector settings, between the "Open in Full screen" checkbox and the "Automatic start" checkbox".

If I understand you correctly, the correct "Projector" behavior should be:
1) The "Automatic start" checkbox" should bypass the "turntable" animation and present the first slide without starting automatically the slide show.
2) The "Open in Full screen" checkbox triggs full screen only once the user has pressed the button "Start slideshow", following step 1 above.

Did I get it correctly ?

Yes, that's correct.

Here is my usage sequence on my Android mobile, once I have launched the album:
1) Select one image folder.
2) The slide show start automatically (by passing the "turntable" animation").
3) The display is not in full screen (although display is set for that, thus truncated) and the slide show runs. See screenshot posted above.
4) Press e.g. the left arrow: the slide show stops and the left menu is displayed again.
5) Press the "Start slide show" button and everything is fine i.e. it is in full screen mode.

So to me, as the full screen is not supposed to be set automatically, it looks like there is some conflict in the "Projector" settings between the "Open in Full screen" checkbox and the "Automatic start" checkbox".

I think I'd go the other way - keep the "go fullscreen" on slideshow start, but remove the autostart on the slideshow.

I think most autostart things are going away - autostart music is virtually gone, and autostart videos work only sometimes. Let the site visitor decide whether he wants to see a timed slideshow or not - don't force him into it.

Laza ... any update to our both feedbacks ?
Thank you for your feedback.

Thank you for your feedback !

Any update ?

Great, thanks Laza.

Btw, I hope everything is fine on your side .