I monitored things and eventually found that the package was scanned in at 11:45 that evening. Kind of late, but still on the same day. So my PO, at least, apparently does scan items as they are sorted and sent out, even if they're in the "drop it and run" bin (where I see lots of eBay and Etsy labels).
From what you're describing here, your post office is not doing any scans at all. If the wording is "Accepted at Origin Facility" or something similar, your package did not actually get scanned by anyone until it reached your regional sorting facility for outbound mail. An Origin Acceptance will list the package's Ship From ZIP location (your local PO's town, derived from the barcode you generated) as the location of that scan, even though it actually took place at the sort facility. All other scans log their actual location. Every timestamp is the actual (local) time when it occurred, even if it gets uploaded late.
So basically, your post office is slacking. 
They did at least get their outbound mail out of the building that evening (probably no more than an hour or two at most after the last collection of the day), and the 11:45 scan would have been its first after the regional truck doing pickups from the local POs finally arrived at the origin sort. The sort facility has to get everything out of there by the early morning hours and on its way to its next stop along its travel (or else they'll get a creeping backup building higher by the day), which it sounds like they did, so in other words, your package didn't get delayed, but that Acceptance scan should have happened before it left your post office.
For comparison, with your next outbound mailing, stand in line and/or do whatever it takes to get the Acceptance scan done in front of you when they take possession of the package (which is when it's supposed to occur anyway), and you will see a different initial sequence of tracking scans for that shipment.
