What is your procedure to 'bulk install'?

The procedure we currently follow for bulk installing the modules is:

• Copy the module .zip files into the: /install/Module folder
• Navigate to: https://www.example.com/i...ode=installresources
• After loading the modules should start installing, but here we are getting the error.

Maybe an important thing to add, we have been able to execute this procedure of bulk installing modules without any problems on different Azure App Services, so it looks like this issue on only existing on the App Service we are currently trying to upgrade our modules.

Yes, that is the correct way of doing this but there could be dependencies. If I install modules that way and for example I install Module-A but that module depends on Module-B I would name the modules like this:
1.Module-B and the one that needs to be installed after that I name 2.Module-A

You can only use that method of bulk installations during an upgrade.  After the upgrade, that feature is deleted by DNN itself for security reasons.  

On a production website that's not undergoing an upgrade, you can do a bulk installation of extensions using PolyDeploy.   

https://github.com/DNNCommunity/PolyDeploy

You can copy back the files needed (just compare the install dir) and once you run https://www.example.com/i...ode=installresources the files that should be deleted are deleted. I use this method all the time.

Mariette is indeed correct, that's also how we usually bulk install modules.
The modules we are currently trying to install don't have any dependencies to eachother. Let's give an example:
We have 2 environments (Environment A and environment B), both environments are a separate Web App.
When doing this on Environment A, we can succesfully use the bulk install method. However, on environment B we are encountering this issue. As far as we can see, the web apps are the same and the DNN database also has the correct settings in the tables.

Could this has something to do with rights for the file system that environment B doesn't have? Because that's the only thing we can think about that might be different between the environments, but we're not sure unfortunately.

I've read a little bit about PolyDeploy, but haven't used it yet for deploying modules, thank you for this suggestion. I will try if PolyDeploy will solve this issue we are currently having.