I can't speak to how it works on the browser as I'm using a forced version of firefox (they borked the new version) however if it's not allowing you to select 'this thread' etc then it's likely your device doing that weird fullscreen keyboard crap a lot of them do. I just installed and tested firefox beta and it worked for me. that's why I tend to think it might be device focused? what keyboard are you using? and device?
When it works: There is a pop-up dialog box with a dropdown with choices, one of which is "This Thread". That is the only place I've seen to limit a search to the current thread.
In three browsers on an Android tablet, in portrait orientation, there is no text box on the top line of the page. There is a magnifying glass. Tap the glass, the top line gets rewritten to <"X"><text box><gear wheel>. Tap the text box, the keyboard opens, but no dialog box. Tap the gear wheel, nothing happens.
When I say I can't select "This Thread", I don't mean it shows the option in a dropdown but doesn't recognize my tapping on it. I don't mean I see the collapsed dropdown, but can't get it to open. I mean I do not get the dialog box, so I do not see any way to limit the search to a single thread.
I do not recognize the reference to "weird fullscreen keyboard crap".
I'm using a Samsung Galaxy Tab A, Android 9. My "keyboard" is the pop-up, on-screen, touch keyboard that came with the system, so maybe Samsung, maybe Google. The keyboard is the full "width" of the screen, and half the "height".