Within Gmail I have rules set up to label my emails. However, within Mailspring I want the inbox to show only emails that do not have a label. Is that possible?
Currently all emails show in my inbox, including the labelled emails.
The Gmail model that Mailspring mirrors is: the Inbox is just another label, and a message shows in the inbox until that label is removed. There’s no “hide labelled mail from the inbox” switch; what you want is for your filters to archive the mail they label, and then the inbox naturally contains only the uncategorised messages.
The easiest place to do that is in Gmail itself: edit each filter and tick Skip the Inbox (Archive it) alongside “Apply the label”. Gmail applies it server-side as mail arrives, and Mailspring picks up the result. If you’d rather do it in Mailspring, create a rule in Preferences > Mail Rules with both an Apply Label and an Archive action — that’s the equivalent, with the caveat that Mailspring’s rules only run while the app is open (Automate your inbox with mail rules — Mailspring Documentation).
For triaging what’s left: there isn’t a -has:label search, but once labelled mail is archived, in:inbox is:unread gives you the unlabelled unread pile, and is:unread NOT in:"Some Label" works for excluding a specific label. One thing that can’t be done from any IMAP client, unfortunately, is filtering by Gmail’s Primary / Promotions / Updates tabs — Google doesn’t expose those categories to third-party apps (Does Mailspring support "Categories" from Gmail or "Bundles" from Google Inbox? — Mailspring Documentation). If you rely on them, a Gmail filter with category:promotions (etc.) in “Has the words” and “Skip the Inbox” turns each tab into an ordinary archived label you can then work with in Mailspring.