Coming at this from a small sample size, every time I've seen it used has been because some of the developers on a team love it and think it's cooler than the other options. And, over time, the operational experience has gotten better (AWS' Postgres support for RDS/Aurora is all recent, for example); and, in fairness, I'd take psql over SQL Server any day of the week.
Regarding why it has popularity beyond mySQL/mariaDB is still a confounding mystery as far as I'm concerned. The additional behaviors Postgres tends to encourage (I'm looking at you, publisher/subscriber and trigger functions) seems to lead to devs advocating it as 'easy' while those in my position are left to keep the damn thing running.
I developed my preference for PostgreSQL years ago, before MySQL supported foreign key constraints or defaulted to durable commits. MySQL also had this annoying tendency to silently store invalid timestamps as zero. All of these things have been fixed since (I hope?), but I still can’t shake my impression that PostgreSQL takes correctness more seriously.
Regarding why it has popularity beyond mySQL/mariaDB is still a confounding mystery as far as I'm concerned. The additional behaviors Postgres tends to encourage (I'm looking at you, publisher/subscriber and trigger functions) seems to lead to devs advocating it as 'easy' while those in my position are left to keep the damn thing running.