I’ve got a mix of Tuya and Tuya Local (link included because it’s very hard to differentiate between them based on name). For a while I was having issues with Arlec devices going unavailable with Tuya, so thought local might help - it didn’t. So I didn’t convert any others.
The Tuya integration is easier to set up, and is done once for all devices, rather than for each like Tuya Local. And I’ve had no problems with the speed/reliabliity of the cloud service (ymmv).
One of the key things to understand for Tuya is the difference between skinned apps and HA integrations.
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Hardware suppliers provide a skinned version of the Tuya phone app to try to keep you buying their products. So if you buy 3 from different suppliers, you can either have 3 different apps running on your phone, or the generic one from Tuya. To complicate matters further, Tuya themselves provide two versions - Tuya Smart and Smart Life. So firstly, you should be using one of the two from Tuya rather than multiple of those from suppliers. I’m using “Tuya Smart” from before “Smart Life” existed (I think, it’s very confusing).
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There is only one official Tuya integration for HA, but anybody can create their own version too, which is how we’ve ended up with more than one “Tuya Local” / “Local Tuya”.
To (hopefully) clear up one other matter, there is a thing called Tuya Convert which can replace the Tuya firmware on devices with Tasmota. This would then work with the HA Tasmota integration. This doesn’t work for all Tuya devices, and unless you’ve got a lot of other Tasmota devices, there should be no need to go down that path.
To summarize - one of the benefits / weaknesses (depending on your view on any given day) of white-labelling and open source, is there can be many ways to skin the cat, and Tuya is a prime example.