I'm 100% new to Premiere Pro as well as any type of video editing software so this might be a fairly obvious answer but I tried browsing the forums but couldn't find anything.
Simply put I'm looking for the best way to save a roughly 10 second clip I put together in premiere that I want to use as a common introduction for all of my future videos in a series I'm making. Right now I have this 10 second clip saved as a project. I'm assuming theres some sort of way to save this as a template possible that captures all of the specific timeline spacings, effects, etc... so I can more or less just drag and drop the entire 10 second clip with all of its settings I created at the beginning of all of my other projects so it starts them off. I didn't see a way to import 1 projects contents completely into another project and I'm assuming that isn't the right way to do it.
You can import complete project files into a new one. However, if you simply want to create multiple videos, you can create one sequence per video, within a single project. Either copy/paste items between sequences, or start off by duplicating an existing sequence and edit onwards from there.
yes you can "import" a project into a new project.... and that's what you do, use file: import rather than file: open. And when you do this, premiere will ask you if you want to import the whole project or... wait for it... a single sequence which is what I think you want to do. You can also have multiple projects open at the same time and simply copy the sequence in question to the new project... btw, when you import a sequence it will automatically import all the source media for that sequence. That's the Premiere works, all media used in a project must be included in the project.
Also, you can just export this clip to a high quality codec like prores422 HQ and then just import the clip into your new project. And if you need to make changes, then just import the sequence... as described above.