AWESOME EXTENSION.
It is working as of August 2020 with the following add-ons installed to Firefox (not mobile):
[] Tree Style Tabs +
[] Tab Unloader for Tree Style Tab +
[] this: Move unloaded tabs for Tree Style Tab

Setup:
[] Tree Style Tabs -- default settings
[] Tab Unloader for Tree Style Tab
-> options -> Tab Hiding -> check "Hide unloaded tabs with the tab hiding API." & grant permission.
-> options -> Tab Hiding -> UNcheck "Suppress special behavior in Tree Style Tab regarding hidden tabs."
-> options -> Tab Hiding -> check "Show hidden tabs in Tree Style Tab's sidebar."

Either of the last two options will display unloaded tabs in the Tree Style Tab sidebar. Disabling both of the last two options will result in unloaded tabs NOT being visible in the Tree Style Tab sidebar.

No glitches with the above setup, 5/5 stars.

Thank you developer.

--------------------------------------------------------------
Lengthy explanation as to why (for the curious:)
--------------------------------------------------------------
I say to disable the 2nd option above and enable the 3rd option because:
with the 2nd enabled & the 3rd disabled, this add-on technically does work for moving unloaded tabs within the sidebar, BUT it glitches and after moving an unloaded tab, it will disappear from the sidebar list.

Tapping F1 to hide the sidebar, then tapping F1 again to show the sidebar refreshes it and DOES make the moved&unloaded tab appear where the user dragged-and-dropped it.

However this is glitchy and disabling the option "Suppress special behavior in Tree Style Tab regarding hidden tabs." and enabling "Show hidden tabs in Tree Style Tab's sidebar." works as intended and no refresh needed.

Unfortunately does not work anymore.

seems the TST has lost the ability to move tabs without focusing on them in some recent update, and this addon does the job well!

Simple but improves TST performance a lot for tab hoarders like me!

do the job !

awesome!