Interesting puzzle solved: page authors complained that some of them face an issue when they try to insert a Microsoft Stream video via embed code in the page body:
The message clearly points to missing of 'AddAndCustomizePages' permission for the logged-on page author. However, on checking the permissions, all the authors / editors do have that permission via an assigned 'Content Management' permission level. After some trial-and-error, I discovered the SharePoint internal cause. The below error message on trying to insert a ScriptEditor webpart in the page content, led me to the Eureka insight:
This site says... Aha: In the site the permission inheritance is broken, to achieve that page authors can only create and modify page (= news) items, but are restricted from modifying anything else in the site. The 'Content Management' permission level is for that purpose not assigned to them on site level, but on the Pages library. On required permission for their author task this assignment is sufficient. But a flaw in SharePoint is that it checks in the 'Insert Embed-code' handling whether the 'AddAndCustomizePages' permission is granted to the logged-on author on site level.
With this insight / understanding on SharePoint level, the fix clear: make sure that all the page authors are also granted a permission level on site level that includes the 'AddAndCustomizePages' permission. And with that fix, all page authors are enabled / authorized to user-friendly apply 'Embed Code' in page edit mode: