Had a plumber come check on my leaky toilet. Turns out the Douglas valve is cracked and leaking. It's an older commode (Oct 2005).. it's a vitromex 6 LPF / 1.6 GPF. The plumber told me the Douglas valve is part of the tank and can't be replaced (so an entire commode replacement is needed. I haven't taken the tank apart yet to verify this, but eyeballing it I can't imagine they would have designed a ceramic commode with a plastic piece that can't be replaced. I'll add some images in a post below for reference.