This is very much “your mileage may vary” question because Apple don’t tell us mere mortals what they do with their syncs, but for what it’s worth mine nearly always works on second try if I wait a couple of minutes. In fact I don’t think it’s not worked on second try for many many months.
I’m also on a VPN (NordVPN) and I have private relay turned on. I’m not willing to sacrifice my privacy just to access DTTG but in any case since for me iCloud sync always resolves if I wait a few minutes I don’t consider it a priority I need to address (it is 100% a priority Apple should be addressing, but I can live with their nonsense in the meantime).
I only get an error a couple of times a day though, I realise there are other users getting it more (and many not getting an error at all) so what I’m willing to tolerate may not be true for someone else.
(I find these threads about CloudKit quite tiresome since it would be worth directing our ire at Apple since they’re the only ones who can fix their shitty sync system, but since Apple don’t care and DT respond, I get why people don’t. But anyway you asked a question and it was deserved an answer. Whilst identifying the root cause of the problem serves no purpose, and no-one asked for my opinion, I am going to say that I believe all of these problems started with Apple rapidly rolling out syncing services to third party apps many years ago. Their infrastructure clearly couldn’t cope with the load, they were quite obviously chasing money at the expense of good service, and now I suspect they have a debt of infrastructure work that they can’t hope to repay because of the scale of the work involved. So we get left with them fiddling around the edges trying to maintain their network in patches, and variable service as a result.)