Over how much time and how does that variable relate to the actual length of time an epidemic of an (apparently) seasonal respiratory virus is expected to last?

I don't think it's just a nitpicky minor thing. Governments have pretty regularly been making decisions and citing the value of "R" (they mean Rt), or "exponential growth", as a justification for new restrictions, apparently without realizing that by itself these things means little and justify nothing. Exponential growth can only be said to be a problem when taking into account the serial interval, the actual exponent, the starting population sizes, total population sizes, fixed capacity limits (e.g. hospital bed counts) and so on. Yet the scientists advising governments routinely ignore all those things.