this is an excellent detailed and knowledgeable article on understanding what's meant by a machine pol in NY and Eric Adams as one

The Company Eric Adams Keeps

He’s the candidate of old political-machine guys like Democratic fixer Frank Carone. What would that mean in City Hall?

By David Freedlander June 17 @ nymag.com

. He only switched to Republican when it was of tactical benefit within NY state politics and everyone involved (i.e., public worker unions,  big real estate money) gets that, gives it a mulligan. Doing the type of switching that Adams did in the state's politics is just seen as being very savvy, as in: a dangerous but savvy player of the machine. You really are dealing with a Tammany Hall type situation in NY state, it's not the same division of Dem vs. GOP as elsewhere in the country, it's not so much about ideology is the thing, it's more "pay to play" and fighting over financial constituencies, not ideological ones (heck even the Hasidic Jews basically do the "pay to play" thing, very cynical voting deliverance by the rebbes-i.e., you scratch our back, we'll scratch yours, what they end up getting: lots of welfare for big families! lots of mulligans for that, too.)

Things just aren't as ideological here, that never has played as well as many other places in the country. (This is why the media thought someone like Yang would do well, BTW). If you think back to the state's history, this goes all the way to before there was a country, this is practical Dutch capitalists starting a sin-filled colony based on money making while all the others either got some religious issues with the English crown or wanting to be a farming gentleman just like they couldn't in the old country.