Thanks to Captain Parker and E. Harding, they were telling me the answer to my previous query, but I was not receptive until yesterday for some reason.
Here’s a chart showing the drop in official “total reserve balances” and how it is largely explained by a rise in Treasury deposits (with the Fed) and reverse repos (that the Fed engages in with Federal Home Loan Banks and other institutions that aren’t eligible to receive interest on reserves):
So, it’s not that reserves are leaving the banking sector, it’s just that some are being held in different ways that don’t get counted in the normal metric.
For a great explanation of the mechanics/accounting of how the Fed is actually raising interest rates, see this Econbrowser post by James Hamilton. (Again, thanks to Captain Parker for the link.)