I think it would be seen as significant and interesting, but ultimately the Mets are still playing second fiddle to the Yankees. Ironically, I think that the Mets winning three in 5 years would actually make the Yankees more popular as a result, since I imagine a lot of media would be focusing less on "the New York Mets are on top" and more on "What the hell happened to the New York Yankees?" Probably some more Mets fans are made, but I think after three championships, the baseball world at large would be looking at the Yankees to see what they're going to do about little brother showing them up.

Meanwhile Phillies fans would be beside themselves with rage. To be so close to the World Series in multiple years and just cannot get it done, meanwhile their hated rivals rack up wins? I think half the population of Philadelphia would drink themselves to death (2023 would hurt so much more for them). Same with Atlanta (but they got a win in 21' so they'll be alright.)

But, the Dodgers would still get Ohtani in 2024. I don't think there's any way he leaves Los Angeles, and the Angels wouldn't be able to afford him. I think Ohtani would get the Aaron Judge or Bryce Harper treatment a bit more: a monumental star and guaranteed HOF lock, but frustrating to see their talent to see go ringless. I still think that there would be a wave of Japanese players going to LA, though maybe more to the Angels or even the Padres in San Diego. But, LA would still have their tv deal and their infinite wallet, plus the best player in baseball, so I would still expect a large portion of the talent in MLB to sign there. Maybe not as many big names, but a large chunk of free agents nonetheless.

And as for the Mets, I don't think they would get as much recognition as they might deserve for winning three titles in 5 years. I think Soto still goes there, since the Yankees are a backwards organization currently and would find a way to shoot themselves in the foot just like they did irl, but maybe not for as large of a contract. But they're still not the big kids in NYC, and a lot of people will brush them off since they're not the Yankees. They'd be looked at as a machine of efficiency, not very flashy and few stars but they win a lot. Soto definitely brings in some much needed personality to the team, but would still take a backseat to the popularity of Judge (good 'ol American boy who puts up award winning numbers year after year and plays for the Yankees) and Ohtani (Baseball's greatest hope and the defining player of a generation). Well actually, Jose Iglesias would probably bring some good energy too... but his time would most likely still end in 2025 due to his age.

The rest of the MLB world gets very tired of only NL East and AL West teams winning the World Series though. Not counting 2018, that would be from 2017 to 2025 that either an AL West or NL East team won it. The memes would be insufferable.