Your sources sound like rubbish.
Please provide links.
The Galileo issue was NOT about a flat earth.
it was about whether or not the sun and planets orbited the earth or not.
That view was certainly disseminated by the Church for 1500 years as it was the assumed science of the day and the Church believed the Dogma of inerrancy of the Bible rested on the geocentric model (as witnessed in the Bible).
That qualifies as a “teaching” in my book.
But Church teachings can be fallible (eg limbo, Mary never died) or undecided in my book also.
However some staunch Catholics, without strong evidence, believe all teachings must also be “doctrines”. That appears an extreme view that is not widely accepted.
Doctrines are considered perennial teachings that will never change even if not formally defined like a dogma.
The meaning of “dogma” is clear enough.
There are very few defined.