"I used this example to show that the first home purchase is not an exception for the 5-year rule,"

Let's restate it properly. The Early distribution of Earnings is subject to income tax, if there has not been a Roth account open for at least 5 years. That is only one of the 5-year rules and those are the two Conditions (early, earnings) that apply. It doesn't matter why you take that distribution, and attained age doesn't matter, either. Nothing else matters.

"I was mistook the 2016-2019 direct contributions as conversions"

Yes, you did.