Although that indicator is there if you remember to look at it, in turn based games it's very very easy to forget to look, and think you're in round 2 when you're actually at the end of round 3. Even though I'm a very experienced photosynthesis player on BGA, even I still do this sometimes. Several months ago I lost a close game because of this mistake, and just today I made this mistake again, although this time I was far enough ahead that it didn't change the outcome.
Especially for turn based games, it would eliminate a fair amount of frustration if this game gave a much clearer hard-to-miss warning when the game is nearing the end and about to end. There are two feature requests already filed for this:
https://boardgamearena.com/bug?id=79061 - "turn counter"
https://boardgamearena.com/bug?id=158166 - "Bold warning for last and next-to-last turns"
Please click through and vote for both of these?