My seedlings sit in water every day, on heat mats with lights. I don't know if I'm doing it "right" but my plants look amazing.
I wouldn't worry at all about water filling up the bottom tray, but that's just one opinion.
My pots are 3 inches high for reference in this photo.
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Thanks for the reply. Like I said, I'm just learning a lot this first year of growing seedlings to transplant.