Rulebook is made by one person and developed in the open. The fastest way to get something fixed is to open an issue.
Include whatever of this you have — it usually decides how quickly something can be fixed:
Please don't paste message contents or full email addresses into an issue. A rule's name and the shape of what failed is nearly always enough.
Sign-in is presented by Microsoft, not by Rulebook. If it fails before the Microsoft page appears, the app couldn't start the request at all — worth an issue, with the message you saw.
Some tenants require an administrator to approve an app before anyone can use it. That approval is theirs to give, not something the app can work around. The error names the app and the permissions, so it can be forwarded to whoever administers your tenant.
Sign out from Manage accounts, which removes the token from the phone. To revoke the grant itself, use account.live.com/consent/Manage for a personal Microsoft account, or myapps.microsoft.com for a work or school account.
Three different things get reported that way. Rule is in error comes from Exchange itself. Folder is missing means the rule files into a folder that no longer exists — Exchange still reports that rule as healthy, which is why Rulebook checks separately. Never runs means an earlier rule stops processing before this one is reached; moving it up fixes it.
Your administrator owns that rule. It can be read but not changed, disabled or deleted, so those controls are shown inactive rather than failing when tapped.
Outlook rules have no negative match. Exclusions are expressed as exceptions instead: add the thing to the Unless section, and the rule is skipped when it matches. This is a limitation of the mail service, not of the app, and works out the same way.
Rules run top to bottom, and one carrying "stop processing later rules" ends evaluation for that message. If a rule seems to be ignored, check what sits above it.
Edits apply on the phone first and are then pushed to the server. If the push fails, the change is kept and the rule is marked as not saved yet, with the option to retry or discard — a dropped connection never silently undoes your work. Deletes are the exception: a rule that looks deleted but is still filing mail is worse than an error, so a failed delete puts the rule back.
Rulebook stores no mail. It reads and writes rules on your mail server, and those rules keep running when the app is closed. There is no Rulebook account, no analytics, and no server of its own — the app talks only to Microsoft.
Reading your folder list requires a permission that also grants message senders, recipients and subjects. Rulebook does not read them, but the grant is broader than the app's use of it, and why that is is worth knowing.