I managed to solve it!
Note: Again, just as a reminder, this is specific to Mac.
So, as I suspected, I was simply creating and accessing SSH tunnel incorrectly. The syntax just needed some minor twist to the one suggested in the Access The Server Using An SSH Tunnel.
What I did instead was:
ssh -N -L localhost:3000:localhost:3000 -i <PUBLIC_KEY_FILE>
This then allowed me to access the port, on the server, via
localhost:3000 within the browser.
And that was it.