When creating a template project, is it possible to set MQSERVER Environment variable somewhere in the project, so it points to a different MQ Manager depending on the project?

Then when the project is distributed, the corresponding MQSERVER Environment Variable has to be loaded for the specific project.

As it is written in the product’s documentation:

In the few cases where the table says to continue using the environment variable, you need to set it before starting the IDE - for example, by starting the Mainframe Express Command Prompt and using the command line to set the environment variable and to start the IDE.

So you can create a .bat and place it in the project folder. The .bat file has to contain the following rows:
set MQSERVER =< MQ_Manager >
mfe

Before to open the template project, the user has to start the .bat file first, so the MQSERVER Environment variable is loaded