Honestly, I suspect it'd be vaguely but definitely similar to OTL's history:
1) Dutch New Netherlands didn't last THAT long in the grand scheme of things. It started in 1624 and was captured in 1664, and was always very underpopulated. Even its biggest boost came only shortly before the capture, to say nothing it had a large chunk of Yankees living in it already. It was noticeable to New England, yes - but could never threaten it at all, the way it absorbed New Sweden.
2) Plymouth Colony itself was already a sect of Puritans who were a bit separate from mainstream Puritans in belief, but they, like the Dutch, were on the more trader-commercial side (they founded Cushnoc, Maine as a fur-trading settlement and scouted Connecticut for the same purpose), and vaguely more tolerant. This harbor is everything they'd want in a traders' dream. *New Plymouth City like NYC will be a commercialized city from the get-go, attracting all sorts of people the way New Amsterdam did. Still definitely English/Yankee, but genuinely more cosmopolitan and financial than New England proper, even OTL Plymouth Colony (who had many non-Separatists in their midst for settling purposes compared to the Puritans Proper being almost ENTIRELY Puritan).
3) OTL Plymouth Colony was already erring to religious tolerance and even freedom, and barely DIDN'T pass religious freedom locally around the early 1640s. I can see *New Plymouth Colony/City passing it with how much more people it would have by default, as well as the more varied populace supporting it.
4) The Province of New York in our world was already lagging behind New England even with its favorable harbor and financial prospects, I can't see why NPC would be different, especially considering Plymouth Colony in OTL already lagged behind Massachusetts and Connecticut population-wise.
5) New Plymouth probably claims New Netherlands' OTL claimed border of the Delaware River, which was partly why it conquered New Sweden. Sweden ignored the Dutch claims, here the powerful and local expanded New Englander presence (via NPC and their direct connection to the other New Englanders) will force them to ignore the area. So OTL PA/DE/NJ are probably officially part of New Plymouth Colony/City, but completely unsettled - then in the royal takeover of New England charter-wise in the 1660s gets split off and given to William Penn and the New Jersey proprietors ANYWAY.
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Essentially? It's an English-founded-and-controlled New Netherland to me. Differences in the details, yes - New Plymouth will definitively be considered New England alongside OTL New England Proper. It'll be a bit chunk less ethnic than New Netherland. The English won't have to send a fleet in 1664. The Plymouth Colony legend will be even stronger in TTL since New Plymouth will still exist. It's fun to imagine the northern USA will have its "first settlement" also be the absolute biggest the way such things happen in a Civilization-style strategy game.
But the Plymouth colonists were probably the most ambitiously commercial of the Puritans, just the way the Dutch colonists were commercial; and they had trouble raising population and attracting immigration just the way the Dutch colonists compared to the Puritans Proper that founded all the Yankee colonies from Boston; and they were quite tolerant compared to Puritans Proper, which may allow small amounts of non-Puritan immigrants to settle there and give a more cosmopolitan feel to the colony versus Massachusetts or Connecticut (and like Rhode Island, by contrast). It'll be given a royal charter in the Restoration since it's too big to ignore compared to reality, and that'll take away its non-*New York land since it has Long Island+the Hudson Valley already. In a lot of ways it's just to me New Netherlands, just under English control from the get-go and a bit less ethnic and tolerant at first, and gradually taking up more and more of OTL New York's character due to its wonderful geography and Plymouth Colonists' ambitions actually being fulfillable and their own initial tolerance gradually expanding.