I would like my folders to individually save the view and sorting options, but those settings seem to be linked to the tab instead.
You might have turned on the Format Lock. You can see its state and toggle it via the Folder menu:
More generally, the usual rules for Folder Formats are what determines those things, and folder formats are generally tied to paths not to tabs.
Thank you, that was it. I've been procrastinating on finding a fix for this for probably a year now.