Cannot give specific answers to your queries, but can answer at least one general.
When Columbia Presbyterian and New York Hospital/Cornell merged the places that were union remained, and those that weren't largely did not.
IIRC New York Hospital wasn't union before the merger, and still are not. OTOH Columbia Presbyterian was and still remains a union shop.
You might be interested in this: https://allnurses.com/which-hospitals-recommend-nyc-t368320/
Prior to being taken over by Northwell (then North Shore-LIJ), Lenox Hill's nurses aides, techs, etch were represented by 1199, which one assumes continued thus still remains so. Same union represents "unlicensed" staff at Columbia-Presbyterian IIRC.
1199 is a strong union and has done well in extracting benefits from hospitals for their members. IIRC the same tuition reimbursement and whatever else you mentioned at Lenox Hill also applies to Columbia-Presbyterian. In fact (again IIRC) Columbia Presbyterian by contract with 1199 reserves a portion of all new graduate positions for union members who have recently graduated nursing schools/become newly licensed RNs.
Far as getting more direct insight you might have better luck in speaking with NYP-Weil Cornell nursing assistants in their native habitat. That is find some going to or getting off duty and strike up a conversation. The SAS (Q) train at shift change times is full of NYP nurses and aides.
Am not suggesting you lurk about the 72nd and Second subway station, but then again..... *LOL*
As for union versus not as with any job you have to sit down and see what works for you . If planning on attending nursing school tuition assistance is something worth having. But how much is it, and is it worth having?
If you've never attended college previously chances are between NYS aid (TAP) and Federal (Pell) most of your tuition will be covered. Addition of (hopefully) limited federal student loans can cover the rest. This is especially true if you plan on attending a CUNY or SUNY nursing program. OTOH if you're aiming for NYU or another private school, that will be more expensive, and require more comprehensive financial aid package.
Since you seem not planning on being an aide your entire healthcare career, know that usually the same union does not represent both nurses and unlicensed personnel. So in four or so years (upon completion of nursing school, passing the boards), you'll be looking at finding new employment as a RN, and thus probably asking these same questions all over again.