The difference isn't long term vs short term. It's capital gain vs income.

There is:

Primary residence: buy and perhaps fix, and live in.

Own and operate rentals: buy and perhaps fix, and rent.

Flip: buy and fix and sell. This comes in two flavors:

As Sched C or other business entity reporting = you intend to do it as your business or side hustle.

As a one-off, that isn't business and isn't residence, but is investment as Sched E.

If you buy, fix and live in it, you have your total cost as basis. If you buy, fix and rent, you have your total cost as basis. If you buy, fix, and sell, you still have your total cost as basis. Nothing changes about the total value invested.

What did they do for tax reporting in the other years, while still owned and not occupied (not a primary residence and not a rental)?

For the funds invested, that is work in process as Asset value; think of this as Inventory or buying shares of stocks that you hold. Purchase cost and improvements are all part of basis.

I've never seen anything that requires a qualification such as "almost 65% of the remodel costs were incurred within 12 months of the sale" or that $90k was in the 12-month period prior to the sale. Are you trying to make this two different assets? There is just the one property.

You have Basis from the purchase cost (in 2016 or 2017?) and adding to that is the Improvements that are increasing the total invested. Sold in April 2019 means held for more than one year.