Given that your upgrade process is supported by Microsoft and you are asking about Esri's recommendation, this appears to apply for a long term configuration. There is not really much risk in having different OS's for a few hours or a couple days. As long as the ArcGIS Server version is not also being upgraded and the version of ArcGIS you have installed supports Server 2022, you should be good.
If your site can support your current load as a 2-machine site, you can remove one machine, upgrade it, re-add it and repeat the process for the remaining servers until they have all been upgraded.
The removing and (especially) adding process can sometimes be process intensive to all servers in the site, leading to the site being slow to respond or even temporarily unresponsive. You should time these operations accordingly to minimize disruption to the clients.
