So much potential here for a lightweight and fast solution for the disorganized or overloaded power user!
But:
1) Limited and mandatory selection of one of only two (2) keyboard shortcuts (⌘+Tab or Option+Tab) is rough. Either replace macOS' native application switcher or replace a common shortcut for AltTab users who may need to visually see contents of the window they're searching for. (I actually love the ⌘+Shift+K shortcut to essentially do the same thing as the prior keyboard shortcuts, but you're actually one step closer to filtering and finding your tabs since you're in "Search Mode" now and can easily hit the ESC key to exit. I personally think this should be the sole and primary shortcut because you're downloading TabTab to search for and find tabs quickly and efficiently.)
2) It would be INCREDIBLE if you could add support to search through tabs on Superhuman for Desktop on macOS. (They currently lack support for "Tab Management" even though it's their flagship application and a ~Chromium-based/Electron-like desktop application. They are huge and growing exponentially, so your solution could bring much-needed relief for many who use their insanely fast email clients.)
As we're talking Chrome here—it just dawned on me that a natural global keyboard shortcut for TabTab could also be ⌘+Shift+A.
Best of luck, and thanks for taking the time to review some feedback!