The Top-15-Leagues in this case are defined by an old transfermarkt.de filter that is rather outdated by today: Top-7-Leagues + Belgium, Russia, Ukraine, Turkey, Czech Republic, Greece, Austria, Switzerland. These were the Top-15-Leagues a while ago it's not correct anymore as of today with the downfall of Ukraine, Russia, Greece etc. and the rise of someone like Scotland. But if you look at it over the long run, as we do here with the whole 21st century, it's still pretty spot on, because if you look at the last 10 seasons in the UEFA country ranking, this Top-15 still covers the Top-16 with only Scotland at rank 15 who have just overtaken Greece in that regard. The data is complete from 00/01 on, so that's why I started there.
These are all players with at least 510 Appearances in the Top-15-Leagues of Europe 00/01 - 22/23 by outfield players:
671 Joaquín
651 Cristiano Ronaldo
619 James Milner* (still active in one of these leagues)
595 Jesús Navas*
589 Raúl García* and Gareth Barry
579 João Moutinho*
578 Lionel Messi and Timmy Simons
569 Dirk Kuyt, Hilton
555 Fabio Quagliarella
553 Sergio Ramos*
552 Edin Dzeko*
551 Karim Benzema and Ivan Rakitic*
546 Umut Bulut
541 Zlatan Ibrahimovic
540 Dimitri Payet
535 David Silva
533 Raúl Albiol*
532 Olivier Deschacht
529 Steve von Bergen
526 Samuel Eto'o
517 Moussa Sissoko*
515 Luis Suárez
514 Kévin Gameiro*
513 Florent Balmont
512 Jimmy Briand
511 Tomas Hübschman* and Sven Kums* (Watford legend)
And if it weren't for injuries, Saudi-Arabia or coaches disrespecting club legends then David Silva, Ibra, Benzema, Ronaldo and Payet would probably also still play in one of these leagues. Tomas Hübschman is 42 years old btw and playing since 23 years, so he actually didn't play that many league games per season but his longevity gets him on here regardless; in 17 of the past seasons he played 25 league games or less (in his defense, he only played in Ukraine and Czechia which usually only offer a player 30 league games at max to participate in).
What's also impressive is that despite these high figures the majority of these players even played in other leagues too.
The count doesn't include Relegation Play-off matches (France, Germany) but it includes league intern play-off rounds (like in Belgium), so if we look only at more recent seasons Hans Vanaken is up there challenging the unbreakable Iñaki Williams for the 1st place because in Belgium you can play up to 40 league games a season.
Dante has exactly 511 games by now with his appearance in nice brest (but this above doesn't include the current season).
In case you wonder where u/MERTENS_GOAT is in this: He is not here because he spent played lower divisions until he was 22 years old, which is rather old to start playing 1st division football. But if we were to cherry-pick our starting point to 09/10 when he joined Utrecht then he ranks at 7 with 456 games played behind just (in order most to fewest) Messi, Candreva tied with Rakitic, Kums, Griezmann and Busquets. Out of these 7 Griezmann is the only one who didn't spend all seasons in the Top-5-Leagues cause in the first season La Real played in the 2nd division. So if we were to start the count 2010/11 Griezmann would probably lead the list by a mile.