Lol while this may be an April fools joke I can imagine something like this actually being developed.
It would probably be possible to get fairly accurate temperature readings from a pacifier like product, I'm not sure that you can get heart rate, blood pressure and blood oxygen levels from the mouth and lips though the tech in smart watches for this is improving in this area, it may be possible with some tweaking (blood O2 is most likely possible in the lips at least and potentially heart rate). You could probably finagle a way to get breath response from one to monitor the breathing activity levels, add a mic to pick up on snoring or other airway obstructions and using that with a gyro or movement detector could detect sleep status.
It may all sound like some silly and pointless joke invention but could actually potentially be a life saving piece of equipment for monitoring newborns and infants.
Imagine a pacifier that could even just only detect when a baby has stopped breathing or is experiencing irregular breathing while asleep, how many cases of SIDS would that prevent. This alongside regular temp monitoring from an item that actually calms a child rather than causes them stress (like regular thermometers do, anyone whose had a baby can tell you how much taking a temp can upset them.) to help detect ilness or infection onset earlier.
With the capability to sync with a phone giving regular status updates on a babies vitals and when they are asleep/awake etc. The biggest problem I foresee with it would actually be in battery capacity and weight, you wouldn't want a heavier paci in a babies mouth potentially damaging teeth/jaw development and on a device that small capacity is going to be very limited, though with improvements in battery tech (especially in the realm of solid state) this will improve.
Definitely worth any tech company looking into. I know you can already buy mats that sit on a cot mattress that can monitor breathing, movement and external temps etc.