Bill writes:

No, you've done exactly the right thing.

If your baggage isn't checked through you have to get through passport
control to get your baggage and then go through 'groundside security'
again to catch your flight.

Thank you very much to you and others for explaining. Hopefully they
have an easy corrective route for those who followed "flight
connections" not realizing this! (It would be an easy mistake to make
given how, coming to the US and connecting domestically, one gets quite
used to picking up one's bag in flight connections, for port-of-entry
customs reasons.)

-- Mark