It depend on how large your petri dish is.
Unless Romulas has a Coruscant or Trantor level of population (not my impression based on what we were shown) then Romulas's population would only have risen to several billions.
However, if you expand the size of the dish to include surrounding planets, and then surrounding star systems, this would enable the Romulan population to grow over the course of two millenium into the hundreds of billions. If the Empire encompasses multiple thousands of inhabitable worlds, then most would have (compare to modern Earth) relatively low population density.
The Romulans would have "Lebensraum."
Mere land does not ensure the survival of the next generation. It needs to be a veritable paradise for this - and, as per what we're shown, it isn't (most planets uninhabitable, etc).
Which is a prime reason for the Romulan population not to be under forty thousand. They certainly would not have anything that could be described as a "Star Empire."
With a population of 38190 romulans, I'm pretty sure you won't have more than a few VERY SMALL inhabited towns. So much for the star empire.
It might be possible for the total Romulan population to be in the hundred million range and still have them do all the things we've seen and had suggested through dialog. But getting much below that make their society difficult to image.
If the romulans were breeding like tribbles, then they could reach ~1-10 billions in 2000 years. Taking into account their pioneering history, wars - or more mundane causes: accidents, crimes, some not finding mates, etc - every single family must have at least 5-6 children.
In which case, the romulan success in ensuring security and reproductive success for the next generation would be impressive; it would be unmatched in the federation, in any case.