To get to the root of this, I trawled through the previous thread that @yvmuell pointed out:
The cited workaround didn’t work for me, but several people noted that turning off gestures in their launcher(s) helped at least temporarily, so I did that for a start.
The launcher issue made me consider the different launcher apps I had installed: I prefer KISS launcher for its simplicity and small fooyprint, but I also had Lawnchair installed as well as Trebuchet, Lineage OS’ stock launcher.
I uninstalled the former and disabled the latter to avoid conflicting settings, and I haven’t had this persistent problem with the recents screen since.
Thanks to @yvmuell for pointing me in the right direction!