2021 Dev Edition / 2021 30 Day Free Trial

The short answer is yes, you can use the free developer or trial edition in the cloud, just like on-prem.

The longer answer entails a few things that may

help you to be aware of:

• There is not a different installer per the editions of developer, trial, or standard/enterprise.  (And this is  or new to cf2021.) Each is just a licensing difference, and a choice made when installing cf from the one installer (if indeed you "install" it, versus other options in the next point) 
• When it comes to deploying cf on Azure in particular, there are multiple ways to do it: on a vm, as a docker image (supported by cf.since cf2016), or via Azure "app service", which leverages use of a war file, which cf has supported back to cf6.1.
• Of course, other cloud services support vm's and docker images as well, and may support war deployment 
• Those forms of deployment ALL support running as the free developer edition. The docker and war approaches support you providing a license key, otherwise they DO run as the developer editon (with limitations on concurrency, and NOT to be used for production).
• All that said, there's no concept of the trial editon with docker or war file deployment 
• You don't indicate doing either the of the latter two,, so I'm assuming your interest may be in deploying cf on a vm
• Deploying cf on a vm is no different than deploying it on a bare metal machine. Run the cf installer, and you will see the choices I referred to regarding dev/trial or std/ent

As for cf2021 in particular, it seems some clarification may help you in your considering it for cloud deployment:

• the new cloud features in cf2021 are not primarily about how one RUNS cf in the cloud, but instead how cfml can call upon cloud services (whether cf itself is in the cloud or not)
• CF2021 offers a new installer variant, better suited to scripted (and cloud) deployment. While the traditional Gui installer remains, a new "zip" installer is available. But it offers the same choices as I referred to initially regarding dev/trial or std/ent, answered either via script or cmd line prompts 
• CF2021 also offers new modularity, so that only the functionality needed for your app needs to be implemented in the cf deployment. See the cfpm, or package manager, feature 
• CF2021 adds new optional json-based scripted admin configuration, again well-suited to cloud (or any) deployment. See the cfsetup feature
• CF2021 also make the cf docker images smaller and they start faster, which is indeed an advantage especially when deploying in auto scaling, such as the cloud
• Finally, you may have heard that CF2021 had added support for serverless deployment as well (on aws only, not Azure), but that functionality was removed in the weeks after its release. We await new info

So not likely quite the answer you sought, but I hope it's helpful. And perhaps it may lead you ro ask a new question. Let us know either way.