From the discussion in an archlinux forum (https://bbs.archlinux.org/viewtopic.php?pid=1998264#p1998264), it comes out that the problem just occurs when okular is in "text selection" mode (ctrl-4). No pop-up is available is this case when a right click is made on an highlighted text. Though when okular is in "browse" mode is (ctrl-1), the pop-up menu is acessible.
Additional information:
In both mode ("text selection" or "browse"), one can have a pop-up window to edit an annotation by right-clicking on the note in the annotation tab of the sidebar, but this is not very practical/intuitive.

Can you attach a video of this because we totally do show the right click menu on text selection mode.

** Comment removed at request of submitter by KDE Sysadmin **

** Comment removed at request of submitter by KDE Sysadmin **

Both links are the same...

Here is (finally) a small video showing the difference between "browse" mode and "selection text" mode. Sorry for the quite unpolished english commentaries (and the previously sent mistaken links).
https://drive.google.com/file/d/1LmOxcMDwC7yP0kDRAonMy1lD0VlqMy4E/view?usp=sharing

Oh, you meant right click on a highlight annotation while on text selection mode. I misunderstood your initial text and thought you were right clicking on a text selection.

Yes that is somewhat on purpose, ideally we would work further on merging browse and text selection modes, but there are unsolved issues.

I don't consider this really a bug, more of a whishlist.

Ok. If it's not a bug, I see it as a lost feature. My solution was initially to downgrade to okular version 21.04.3 for which popup menu work in both mode, till someone told me that I had to use a browse mode in order to do things related with annotation instead of text selection. I don't find that very intuitive or practical. It raises the question of how people will learn this new restriction for annotation.

Maybe a correct bug would be about the possibly missing documentation that would explain the way it works.

I just compiled 21.04.3 and no, you can't right click on an highlight annotation while on text selection mode either.

I can confirm it and that can little bit annoying: 

When you first used the text selection mode and then use eg the highlighter tool from the toolbar to annotate some text, but noticed that you did an error and want to remove it by right clicking -> delete, it won't work, because the "Selection mode" becomes enabled again, disabling the context menu.

Whilst I have some understanding for the developer's perspective ...
Please reconsider: if something is not intuitive, it is the same as trying to speak to someone in an unfamiliar language. Very frustrating.
I also find that if I do not click in exactly the right place, Okular creates a new text box, and hen I cannot delete it.
I had to do a search to figure this out.
Surely a simple solution with too much difficulty would simply be to add a "delete" function in the right-click context menu? I mean, all the code already exists, doesn't it? And more, this was a function that existed previously - that in itself should be justification.
A case of $1 saving $1,000 of ongoing frustration.

(In reply to Elmar from comment #12)
> Whilst I have some understanding for the developer's perspective ...
> Please reconsider: if something is not intuitive, it is the same as trying
> to speak to someone in an unfamiliar language. Very frustrating.
> I also find that if I do not click in exactly the right place, Okular
> creates a new text box, and hen I cannot delete it.
> I had to do a search to figure this out.
> Surely a simple solution with too much difficulty would simply be to add a
> "delete" function in the right-click context menu? I mean, all the code
> already exists, doesn't it? And more, this was a function that existed
> previously - that in itself should be justification.
> A case of $1 saving $1,000 of ongoing frustration.

I agree. I ended  up here because I thought it was impossible to remove the highlight from a text

For Okular version  21.12.3, I confirm that this works in "browse" mode.

The bug only happens in  "text selection" mode.

A very similar problem still exist in version 22.08.0. I use archlinux package here. The problem appears after sometimes only. When it occurs, if  downgrade to version 21.04.3, it works well back. Strangely if I upgrade back to 22.08.0, it works fine, for sometime and then it fail to work. I did test twice and it ended up failing twice. I'm in my third attempt now.

(In reply to Martin from comment #14)
> For Okular version  21.12.3, I confirm that this works in "browse" mode.
> 
> The bug only happens in  "text selection" mode.

Now, I understand. When it start failing, I have to make a second right click in order to open the annotation pop-up window! Thank you Martin. It does really solve the bug, but it help quite a lot! It make the bug bearable in the sense the annotation is functional with a rather small annoyance.

*** Bug 435918 has been marked as a duplicate of this bug. ***

I think it is important that the right-click + delete works in all annotation modes (highlighting, pop-up, etc.), as this is when it is most needed, e.g. after highlighting the wrong part of text or placing a note in the wrong place. It is very tedious to have to switch out of the annotation mode in order to delete the wrong annotation and then switch back into it again to add the annotation in the right place.  Therefore, I would consider this missing functionality a bug.