I know Eswatini quite well, lived there for several years as a kid, and return as often as I can.

Regarding the shuttles, they can drive fast, yes. I have taken them a number of times from O R Tambo, and also flown too. The new airport is quite modern, (very small obviously, as they only have a three flights a day (or did). The Transmagnific shuttle is one of the better ones!

Bear in mind, the airport is situation in the east of the country, but has a good road to Ezulwini and Mbabane. Ezulwini is probably better for you. I stay at a great place there, can give details if interested. From there, you can visit the former King Sobhuza Memorial Park, the museum, go watch a Swazi dance (very highly recommended), learn a bit about the culture. You also have great views of Execution Rock from Mantenga Lodge.

Very high recommendation from me, is the Foresters Arms, in Mhlambanyatsi, ok, my friend manages it, but it's superb. If you want to rent a car, highly recommend one if you are interested. Also, take time to visit the Malkerns and surrounding areas.