Doas is doa on Linux at least. Last I checked maybe 6 months ago the password timeout feature was still broke. You get asked for the password every single time you run doas even if it was just 2 seconds prior. Maddening. Apparently this has been the state for years now?
As mentioned elsewhere, this is because it relies upon a kernel mechanism that Linux simply does not have, and fixing this involves fixing Linux.
To which I add that it is important not to conflate Jesse Smith's doas, the portable doas that has code for different operating systems including OpenBSD, with Duncan Overbruck's OpenDoas, the "open" doas that is tied to Linux has has had the code for other operating systems removed and mechanisms copied in from sudo for things like timeout flag files.