My nearly three year still has both at night.
Bottle with warm milk before bed, she'll take a cup if there are no bottles but likes to lie down to have a story while drinking it so it's less messy and less bedding to clean stale milk from. I have found even the 360 cups leak a little with her. She then gets up, brushes her teeth, finds a dummy and has another story in bed.
There is no dummy throughout the day at all, and if she takes one (stored in her bedroom) we tell her she has to go to bed if she is tired enough to need a dummy, and we also will not engage in conversation as "we can't hear her with that in her mouth". When we started doing this she weaned herself off the dummy during the day. I find now if she goes for one it's when she's ill / exhausted, and will actually go lie in her bed with it.
I sneak into her room once she's asleep and remove her dummy, but lately I've found it disgarded on the floor anyway as she's starting to lose interest in it.
Ive, for the most part, let her wean herself off these things (with some pressure and guidance) and have found every little problems with it. They will do it in their own time with your help/support - the only thing I'd recommend is not letting them constantly have the dummy in when speaking etc.
For the record - her teeth are fine, her speech is ahead of what is expected, and she's definitely not a "baby" child. 😁