How to transfer an HTTPS site to another server while maintaining availability during the transfer?

Question

Digital certificates

There is a site that opens via HTTPS and it needs to be transferred to another server, keeping all the URLs. An SSL certificate from Comodo is already installed on the old server and it opens via HTTPS.
The problem is that ajax requests via HTTPS from external systems are constantly flying to the site and the maximum downtime for it is a night.
With a site without SSl, everything is clear - transferred files, updated DNS, made a proxy-pass on the old one to a new server and wait until everyone has updated DNS.
How do you do the same with an SSL site? My guess is, just like without SSL, only first issue a second certificate to a second server with the same URL, and then update the DNS.

Answer 1

You just need to transfer the old certificate to a new server, it is not tied to the server in any way, the downtime will be for minutes.

Answer 2

Downtime - a night when transferring a site - is, as they say, a fail.
Set up a new server first (including certificates), then change DNS. Nothing else is needed.