the Joomla system SEF plugin operates directly on the rendered HTML
Not quite like that. Most likely - the Joomla system SEF plugin operates directly on the rendered HTML of com_content, but not of com_sppagebuilder. To work properly, the default menu structure is required.
You can conduct a simple experiment - assign for home page Standard Default Menu item - Favorite articles. Place any index.php?Itemid=629 in the standard Joomla article. And it will work correctly with SEF.
But if you replace the home page to the Sp Pb page, the links within the standard Joomla article will change and stop working. You will need to change them with a new structure. I did not check it with other components, but it will most likely be the same. Because any third-party menu item disrupts the integrity of the content structure of the Joomla by default.
As a workaround, you can try to place links using the ability of the editor, such as JCE. When you assign the link there is the ability to select the menu item.
And of course, this problem requires the attention of the Joomshaper team. For a long time, many users asked to add the ability to assign links as it is in JCE. But while this is not realized unfortunately.