If those are your use cases, then you would probably want to get a Dutch bike (>5k); specifically for a big doggo, groceries and suitcases. Unfortunately there are no North American companies currently making cargo bikes as good at replacing cars as the Dutch ones. Though most people do perfectly fine with North American versions, even with children (but not big doggos lol).
The only good reason to drive a car in the situations you listed is driving it to another city, which would very likely not be feasible with an e-bike. Unless that trip is taken up every weekend, the best (and cheapest) way to accomplish that would be to rent a car.
A good e-bike is certainly a good replacement, unless you focus on certain situations like driving 4-5 hours out of town. Everything else it can do just as well and even make it easier and less stressful.