Source of Issue Discovered
I use Google Messages as my default text messaging app. Today I noticed that a Trash Folder was added to the settings.
Once the messages in the Trash Folder were deleted, they disappeared from Phone Link as well. Apparently, Google just rolled out a new feature that sends deleted texts to a trash folder for 30 days for being permanently deleted instead of being permanently deleted right away.
If anyone is having this problem and does not use Google Messages, I'd say it would still be worth it to see if the app you use has a trash folder too.