When a tab is duplicated using right click option, the entire TST sidebar becomes uninteractable until the new duplicated tab is loaded into TST
TST sidebar remains interactable while duplicated tab is loaded into TST sidebar
TST sidebar shows throbbing animation and doesn't let user interact with sidebar until the duplicated tab is rendered/loaded into TST sidebar
I've never used it before, but I am seeing a similar behavior with only duplicating 1 tab. (Windows 10, FF 66.0.5, TST 3.0.11)
In addition, it appears that the duplicate tab is not made a child or sibling relative to the original tab.

https://bugzilla.mozilla.org/show_bug.cgi?id=1394376 looks like it will land in Firefox 68! (July 9, 2019)
Now the blocking screen effect for duplicating tabs is disabled on Firefox 68 and later, because duplicating of tabs became enough fast.
Looks fixed to me on FF 69.0a1 (2019-05-30) (64-bit) and TST 3.0.15

However the duplicate tab's placement is inconsistent as @irvinm noticed. I will submit another issue soon
Most helpful comment
Related bug of Firefox: 1394376 - Resolve browser.tabs.duplicate() promise right away (before tabs are completely loaded)