Well.... I feel like an idiot. Read the above comments (thank you Siggemannen and Charlieface). I tried refreshing / restarting SSMS but it still marks the linked server as an error (red squiggly line).

I just created the stored procedure, ran a test, and it works. Although...even when I go to modify the stored procedure, it still does marks the linked server as an error/typo... Not sure if that is something I'm doing wrong, but it seems to work now. My OCD may get the best of me by the end of my project, but I'll power through it somehow.

Thank you again