Yeah I've repeated it on Heartland as well. If anyone wants to see, make sure you wait one month after building the second station and the passenger demand (and other house demands e.g. mail) drops at the primary station.
I ran some tests and the passenger demand recuperation is also worse at the primary station when a secondary covers houses in that same area (even when no trains are delivered to the second station)
only one primary station 11 houses
5 demand initially Jan 2029
3 demand after 6 pax car delivery in Mar 2029
Recuperates to 5 demand in May 2030
one primary station and one secondary station
5 demand initially Jan 2029
drops to 4 demand one month later Feb 2029
2 demand after 6 pax car delivery in Mar 2029
Recuperates to 4 in Apr 2031
Recuperates to 5 in Dec 2031
I think for most of the game it's probably better to have just one station because passengers are the main revenue in the game. Maybe consider a second station if highly congested.
Minor: How does this affect competing stations with AI?
You can build stations at where the AI is located. Just by building stations in the same cities as the AI (not even taking cargos) I reduced one AI company's yearly revenue from 2,542,000 to 1,833,000.
Minor: what about 2 stations in one city from a merger?
I also found that deleting the primary station and leaving the secondary station will cause the secondary station demand to rise to what a primary alone station would have had. The secondary station now functions the same as if the primary station was there alone. It probably is best to delete AI stations (from mergers) that are in the same cities that you have.