How do we book a 4 hour, in home pet sit - is that house sitting, dog walking, drop in???

You’re right, this category doesn’t exist. However there are sitters who are willing to provide this.

I’d suggest search for housesitting because drop in visits and walks are generally 30 minutes or an extended rate of 60 minutes. (Some sitters who provide that may also provide housesitting, so they will still appear in the search results.) After narrowing it down to top few choices (rover only supports messaging a few at a time), in the messages to the house sitters you are interested in, let them know it’s for approximately _PM to _PM, that you’re asking them to stay at your home. That will eliminate sitters who are not available to do so.