Now for the question. At what point during this flight did I cease to be
operating under an IFR flight plan? I had assumed that since I had not
requested to cancel IFR at any point that I was still on an IFR flight
plan the entire time.

Per the Pilot/Controller Glossary, as soon as you shot the approach
at Stockton. If I read your post correctly, SCK was your clearance limit.

It seems to me that it depends on whether or not he landed at Stockton, not
just did an approach. The AIM 5-1-13 says:

e. If operating on an IFR flight plan to an airport with a functioning control
tower, the flight plan is automatically closed upon landing.

There must be something about this in the 7110.65, but I can't find it.