To be frank, PostgreSQL has evolved a lot since the late nineties. There was a time where people preferred MySQL over it at it seemed to work faster, certain things were easier and so on.
The MySQL performance advantages were large, with the small caveat that it was fast as long as you were using MyISAM, which achieved its speed by throwing away many safety features, like working transactions and foreign key constraints. Unsurprisingly, when eventually it got an engine that didn't throw caution to the wind, the performance advantage went away.
I spent a lot of time in the early 2000s showing people whose that many of the issues they were facing with their e-commerce websites were ultimately down to the MySQL engine they had picked. But it's faster! Yes it is, but now your application code has to deal with all the things the engine has now offloaded to your application code.
It's not that Postgres' changes were key to increasing market share, but that as MySQL matured, it had no options but to lose its 'advantages'.
I say “was”. I hear it’s vastly better now.
Without these windowless years, PostgreSQL would be the most used RDBMS right now.