You can absolutely do things one at a time. The only possible concerns there are the fact that you'll be destroying one mesh (removing repeaters that other devices might depend on, for example) as you build the other (which in turn may then not yet have a strong enough "backbone" of repeaters for all your devices), plus the fact that you'll be running multiple networks simultaneously and are more likely to run into congestion in the protocols' corresponding bandwidths (but with only two of each that's unlikely; Hubitat lets you choose your Zigbee channel, so maybe make sure it's not the exact same as SmartThings', but also keep in mind possible 2.4 GHz Wifi interference, so maybe keep Hubitat on a channel you're likely to want to use long-term).
If you feel like starting all over all at once, however, you certainly can remove all the devices from ST, making sure they're excluded or reset and ready to re-pair to a new network like Hubitat. Up to you!
If you are using SmartThings, you could consider using the community HubConnect app to "share" devices between ST and Hubitat during your transition. That would allow you to move either the SmartApp/app or thing/device to the new hub while keeping the rest on the original if you're not able to do everything related to a particular device or app at the same time. Otherwise, you could also do things the "old fashioned" way, moving devices (and automations/apps) in a way where the hubs don't depend on each other during the transition (or at least you could temporarily deal with them not).
Regarding "excluding" devices themselves, that is an important consideration for Z-Wave in particular: Z-Wave devices must be excluded from their existing hub or totally reset (usually--I did see a story of one particular old device where a reset still didn't erase the pairing), otherwise they won't want to join to a new hub. You don't need to use SmartThings to "politely" exclude/remove it from that network--any controller, including Hubitat, will do--but that is certainly a fine way to do it if you can. This is also true for Zigbee devices, but they're generally less picky and can just be reset and paired to a new hub, though removing them from their existing hub (using that hub) is also usually easy, often requiring you to do nothing on the device itself (Z-Wave usually makes you press a button once or thrice).
Some people also recommend leaving the old hub powered down when moving. I've never had this problem, but there are apparently reports of old hubs being too aggressive with wanting to re-pair old devices, and that's an easy way to avoid this possibility.