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It only does it for tabs that you've viewed previously (i.e. not restored from a previous session), and not the current tab.

FF 130 does not do that for me by default. I had to go to about:config and set browser.tabs.hoverPreview.enabled to true.

Yeah same, this was off by default until I just toggled it on. Thanks for the tip!

Unfortunately it seems this doesn't work/integrate with TST.