In my neighborhood in NYC, I've also observed that rents increased after luxury apartments were built here. In fact my landlord cited the increased median rent in the neighborhood as a reason to raise my rent.

My understanding of the situation is that luxury apartments do indeed gentrify neighborhoods (i.e. they increase the local rent and drive displacement of locals that can't keep up with those rent increases).

However, across the entire city, it slightly eases rent pressure by providing additional housing supply.

So, like you mentioned, if you get enough housing across many neighborhoods, you can drive down rents. Otherwise, that luxury complex in your neighborhood might only be helping ease rent pressure in other neighborhoods.