That's not what 5G standalone means, as far as I understand.
The network I'm using supports 5G SA in some cells, but my phone definitely still falls back to both 4G and 5G non-SA in some areas where it's not yet available.
And even if 5G SA were available everywhere, there's the concern of roaming.
Correct, your phone needs to actually re-connect between the two networks. It's a whole new session and you can't handover between 5G SA and 5G NSA/LTE networks. There are some configurations that make this not much of an issue, but technically they are totally different networks.
The network I'm using supports 5G SA in some cells, but my phone definitely still falls back to both 4G and 5G non-SA in some areas where it's not yet available.
And even if 5G SA were available everywhere, there's the concern of roaming.