Question about the translation engine

From the beginning, I didn't know how to use the translation engine across several projects. Every time a new project is created, I want to use the same translation engine but not the same TM, and every time I change the project settings, the translation engine will change accordingly. So I am confused about how to use the translation engine ACROSS SEVERAL PROJECTS.

Recently, I found that the TMs can be set to be different for different projects with the same translation engine, but on the premises that the new project is created from the CLOUD. But all those before, I created a new project in the STUDIO, and then the translation engine always changed according to the project settings.

Therefore, could you look into the problem or explain why that is not possible when creating from STUDIO??