Delay in emails being received in K9

On android 13 running version TQ1A.221205.011.2022120700 of GrapheneOS I am seeing this situation:

I have email address – An Outlook email address requiring Oauth2 – and I have a rule set up that all emails received at are kept in the inbox there but are also immediately forwarded to the inbox at email address .

On my android device K9 version 6.400 from F-Droid is set up using OAuth2 for, and the Fair email app is set up for . In K9 the inbox folder is a class 1 folder, and I have these settings:

Sync messages from: any time (no limit)

Fetch messages up to: 2 MiB

Folder poll frequency: Every 15 minutes

Poll folders: 1st and 2nd Class folders

Push folder: Only 1st Class folders

Here is what is happening, I will use a recent email sent to me as a very typical example:

A person sent an email to me, sending it directly to , no other email addresses were included in the distribution of this email. The email was a short paragraph of text only, no attachment. Within one or two minutes of this email having been sent it appeared on my android device in the forwarded to email address of visible in the Fair email application. The email did also eventually appear in the direct recipient email address of in the K9 application on the same android device, but roughly six hours (!) later. I am seeing this kind of situation happen many times with emails sent to . I never see emails sent to show up in K9 more timely than 15 minutes later, but many times there is a much longer delay.

Question: Why would it take between 15 minutes and several hours – but never more timely than 15 minutes - for an email to to be received by the K9 application?