I didn't mention Tailscale. I said "overlay", and both SD-WAN and MPLS L2 VPN are overlay networks.
A change in an IP lease should result in no downtime whatsoever, because addressing is not the same as routing. A routing change would have exactly the same effect on a static IP.
I then pointed out that an overlay network means you don't have to worry about that anyway.
I think you need to reread whatever comments you think you are responding to, as there is clearly something out of sync with your replies.