It sounds like either the current Series 9, or a 3rd generation SE would be the best choice for you. Both are low profile and light, both do the haptic vibration things you want as well as notifications, texts and calls. The advantage of an S9 over the SE is an Always On Display capability, ECG, and Blood Oxygen measurement. If those are not important to you, get an SE.
Neither of those watches will measure up to your battery expectations, and will have to be charged daily. (the Series 9 will charge much faster than the SE though), but you’ll be charging daily.
There’s also the Ultra, but definitely not slim or low profile, and much heavier than the aforementioned two devices. The Ultra however has about a 3 day battery life.