I am an incoming PhD student (for the fall). I recently received a message from a faculty member saying she was impressed with my application and asking if I wanted to talk about rotations. Ordinarily this would be awesome, but the rest of the message listed every grant and award won by this faculty member since 2009 (there were a lot of them), and it really seemed like overkill. Should this be considered a red flag, or is it just a practical way to demonstrate that the lab group is thriving? This is in the US.
I think you may be overthinking this slightly. It’s neither a red flag nor necessarily a practical way to demonstrate anything (although it might actually demonstrate something useful, I have no idea).
People are quirky and sometimes do things that don’t make complete sense to other people, or even to themselves the next day. This is true of everyone - including, I’d bet, you. I’m sure you wouldn’t want other people characterizing every slightly unusual or eccentric thing you do as a red flag.
Since “ordinarily this would be awesome”, I suggest that you be happy a faculty member (who has won many grants and awards since 2009!) is taking an interest in you, and talk to her to evaluate the rotation option as you would talk to anyone else in a similar situation.