Gmail, iCloud, Yahoo or your company's own mail server all connect the same way: your address, an app password, and the server details if we don't recognise the domain. There's no waiting list and no review queue in between.
Most providers only offer app passwords once 2-step verification is on. If you can't find the option, that's almost always why.
Findest checks the mailbox every 5 minutes, so a document is usually filed within 5 minutes of reaching you. Outlook and Hotmail addresses go through Microsoft's sign-in instead, because Microsoft no longer accepts app passwords for them.