After some more research and experimentation I was successful in getting my title sequence from one project into another. The answer, was in fact, via 'scenes'.
Here is the process I took to accomplish the goal (using Blender 3.0.1):
Build your Title Sequence (Scene)
Open a new project in the VSE, add your text strips, and set the key frames to animate as you desire:
Then, it would be helpful to rename the scene. In the upper-right corner of the Blender window, highlight and change the scene name to something meaningful:
Finally, save the project as usual.
Appending the Title Sequence to a New Project
Next, close the title sequence project and open a new/existing project. Then, go to File -> Append, navigate to your Title Sequence .blend file and double click into it. This will not append anything, but instead let you navigate around the .blend contents to pick what to actually append to the new/existing project:
From there, navigate into "Scene", select the scene you named your title sequence, and click Append:
Note: You won't see anything in the new/existing project yet, but you will shortly. Keep going...
Insert the Scene into the VSE
Now, in the VSE, Add -> Scene and select the Title Sequence you created (it should show the name you used):
At this point, you should see a cube in the preview window and the sequence editor will contain the scene strip:
KEY #1: Access the Title Sequence Itself
Now, HERE IS KEY #1 - notice on the right of the sequence editor (shown in the previous image), in the Scene drop-down section you have "Scene" and "Input" labels? Change "Input" from Camera to Sequencer. Your strips and preview should look familiar now!
KEY #2: Access the Title Sequence Strips
Finally, to edit the text strips (text or animation content), open an Outliner pane (the image shows me just changing my preview pane to the Outliner):
Change the "View Layer" to "Scenes":
and click on "World.001" under Title Sequence (or whatever you called your title sequence scene):
And now you have full access to the text strips to modify as you'd like.
Going Back to the Project After Adjusting the Title Sequence
Once you've finished adjusting your title sequence, click "Scene" to go back to the new/existing project and continue inserting/editing the video as usual:
As you can see, I created a new preview pane to show the last step.