> "What would be the best way to go about it?"
Moving your site server to Azure is fine but in no way helps managing clients in a distributed environment as your remote locations [most likely] don't have direct connectivity to Azure. Managing clients in a distributed environment generally consists of
placing DPs at those remote locations which is probably what you already have. Moving the site server to Azure doesn't change this in any way.
Additionally, always keep in mind that Azure costs are based on resource consumption including disk, processor, and outgoing traffic. Thus, while I'm in not discouraging you from moving your site server to Azure and it may be cost-effective in the long run
as there are many intangible costs that most folks never account for with on-premises systems (like power, cooling, security, Internet, etc). With Azure these are monthly, possibly variable costs, that can add up and cause sticker shock as these aren't explicitly
accounted for with an on-prem server.
So yes, moving to Azure can be good for many reasons, but enabling management of a distributed environment is not one of them unless you have configured direct, reliable connectivity from each location directly to Azure.
Jason | https://home.configmgrftw.com | @jasonsandys