List what is unread. list_notifications with the default filter returns unread items. Scope to owner and repo when the request is about one project, and use since when catching up after time away. Page rather than raising the limit.
Group before opening anything. Bucket by reason and subject.type. The shape of the inbox — twenty subscribed comments on one thread, two review requests — decides the order of work, and it costs no extra calls.
Open only what looks actionable. get_notification_details costs a call each, so spend them on the buckets that survived grouping.
Decide using the ranking below.
Clear what is handled. dismiss_notification with state: read for something seen, or state: done to remove it from the inbox entirely.
Stop recurring noise at the source. manage_notification_subscription with action: ignore mutes one thread. manage_repository_notification_subscription does the same for a whole repository, which is a much bigger decision.
Report what is left, with the reason each item survived triage.

Decision points

Rank by reason, then by age:

review_requested — someone is blocked on you. Highest priority, and it never gets dismissed without being handled.
mention and assign — addressed to you specifically. Needs a reply or an explicit deferral.
team_mention — addressed to a group; check whether someone else already answered before treating it as yours.
author and comment — activity on your own threads. Usually read, sometimes a reply.
subscribed, ci_activity, state_change — informational. Read or done unless something failed that belongs to you.
security_alert — do not clear it. Escalate or track it; investigating alerts is a separate piece of work.

Two rules: never dismiss something you have not opened when its reason is review_requested, mention or assign; and never unsubscribe from a thread on someone else's behalf.

Fields that matter

reason — the whole ranking above depends on it, and it is the field most often ignored.
subject.type — Issue, PullRequest, Release, Discussion. Same reason, different urgency.
unread — a notification can be updated after being read; it comes back.
updated_at — how stale the item is, which decides ordering within a bucket.
threadID on dismiss_notification; notificationID on get_notification_details and manage_notification_subscription — use the returned notification identifier, not an issue or pull request number. Repository subscriptions use owner and repo.

Confirm before clearing anything

mark_all_notifications_read is irreversible and hides everything you have not looked at. Do not call it as a shortcut. If it is genuinely wanted, scope it to owner and repo, say exactly how many notifications it will clear and what they are, and get explicit agreement first.

manage_repository_notification_subscription with action: ignore silences a whole repository indefinitely. Confirm the repository by name and say what will stop arriving.

Bulk dismissal of more than a handful of threads needs the same treatment: list them, then ask.

Empty and failure cases

Nothing unread — say the inbox is clear and stop. Do not widen to read notifications unless asked.
Everything is one reason — say so; twenty subscribed notifications on one thread is a subscription problem, not twenty decisions.
A dismissal fails — report which threads were cleared and which were not. An inbox reported as empty when it is not is worse than a partial result.
Details unavailable for a thread — the referenced item may be in a repository you can no longer see. Leave it, and say why.

notification-triage

Triaging a notification inbox

Sequence