On Pages 14.1 x ventura 13.7.6 often the right menu disappears (first time it happen...) Why?

The insertion beam cursor is only valid when you are actively typing in the document or passing the pointer over the document body. It changes to a pointer icon when elsewhere over thumbnails or other areas of Pages that are not body text.

If what you are calling the "right menu" is actually the Format Inspector, then yes, it is normal for it to disappear when you move your pointer out of the body text and click on a thumbnail, and reappear once you click again in the document body.

I cannot reproduce what you describe in Pages v14.4 on Sequoia v15.5. The Format panel remains when I move the pointer off of the document contents. I don't have Ventura or Pages v14.1 installed here now, so cannot test in your setting, though this behavior did not exist when I did have that version of Pages on Ventura.

Did you install any other software before this issue with Pages v14.1 began?