I’ve decided that I will do this new function as a custom post type in the same installation as the college website.
I will find another project to learn and use WP Rest API. It’s an overkill to use WP Rest API on this project.
I also realize that Our Team content is really part of the College website. Logically, it shouldn’t be in a separate ‘database’. It would cause backup, restoration, migration and management issues later if I were to maintain these 2 content separately. The only stage it would be logical to separate the content is when Our Team needs to have functions relating to HR, Operations and Personal (eg: personal blog for lecturer, multimedia resources and such).
To solve the clutter issue, I need to remove the unused CPT from the Premium Theme. Delete unnecessary and unused plugins.
Thanks WPSE for giving me the space to ‘brainstorm’ and thanks Fayaz for your comments.