I really like the way Vivaldi does its F2. I found this extension when I searched for a firefox extension, so thank you for creating this. One very common thing I use F2 in Vivaldi is to quickly switch tabs (since I have too many tabs) by typing the partial site name or url and it quickly filters the available tabs and upon selecting it switches to that tab. Can you please add this functionality! :) This is a huge feature that can really help managing large number of tabs.
I think also that in some screens like addons.mozilla.org the F2 doesn't work. I assume due to some security reasons, not sure if this can be fixed somehow.

I haven't had any issues yet - it satisfies my occasional need for a keyboard-only browsing experience.