It appears that the Properties Toolbar will bulldoze other regular toolbars, but not the ones you create yourself as shown here.
I found that the Properties toolbar (marked green, right) first displaces/compresses other toolbars (also user-created toolbars, here marked blue-ish on the left):
...further compression of left toolbar (when selecting the polygon comment):
...but in the end, the Properties toolbar leaves the custom toolbar alone and instead collapses itself (when editing comment text, where the Properties toolbar would be too wide to fit):
...providing a Properties flyout instead:
Anyway, as long as toolbars in general (thus also the the Properties toolbar) can't be placed in the Titlebar, we'll probably have to live either with having a minimum of two rows of (tool)bars, including the Titlebar, or with placing the Properties toolbar somewhere else, for example freely floating like here:
I only wished the Properties toolbar would collapse even more when nothing is selected (like here), and that the "Exclusive Mode" button could be removed -- I never use it, but have accidentially activated it probably hundreds of times, only wondering what was wrong with my document afterwards.
Edit: the Properties toolbar does
collapse even more -- when the option "show text labels in toolbars" is not active:
This way, I might actually settle for
placing the Properties toolbar somewhere else, for example freely floating like here
...because cramping the Properties toolbar, which can get REALLY wide as we have seen:
...in the program titlebar (together with everything else) indeed might not be the best idea.