2M is not a big city. But it is a city, and one would expect most of the city stuff people are talking about to be available, including restaurants, theatres, museums, shopping malls, supermarkets, hospitals, gymnasia, fairs, clubs, bars, public transport, concerts, industrial zones, maybe a university, etc.
Tell that to my new local ‘city’, Truro…
The things I miss from living in a proper city, as opposed to having a wee baby joke one down the road is definitely the cultural variety; food, music, even clothing. Yeah, we have an Indian restaurant in town, but it caters for Cornish tastes, and their 
is my and their is my 
. After living in a place where there were more than 10 Indian restaurants or takeaways within a 15 minute walk, in about half of which most of the clientele were of Indian background, I’m definitely feeling the difference.
Even pre-COVID, there were only a handful of music events a year that I wouldn’t have to drive at least a few towns over for, most of which were small not-well-known folk groups. I miss the incidental stuff as well; walking down the street and hearing new music, street art, weird events, street markets where it’s not just tat aimed at tourists, people of different nationalities who aren’t just passing through, buses that run often enough to be usable…
Back when I had money, I would leave the city any chance I got, either vacation of visiting family. I always enjoyed coming back though, it’s not like I hated the city.
Having interesting natural areas is essential to enjoying big city life IMO. I spend a lot of time in Central Park (ok, it’s man-made, but anyway…). It’s always the highlight of the walks I take several times a week.
I usually walk 3 - 5 miles which can go by quickly in the city given the entertainment along the way. Plus I can go walking after dark, which is especially handy in the winter. Going for a 5 mile or any length of walk in the suburbs or country in the dark isn’t much of an option unless I’m just stepping out to star-gaze.
My sister came into town and we were looking for something dirt cheap to do so we did a round trip on the Staten Island ferry watching a storm roll in, then took a smaller ferry back up to my neighborhood after dinner. It was dark, so the city lights were really nice.
My daughters like going out to the beach, usually the Rockaways, and it just costs a couple of subway fares and any number of their friends can join in. It’s not this big load up the car and drive for hours thing we used to do when I was little.
My wife and I aren’t big theater-goers but my daughters enrolled in free summer programs where part of it was going to broadway and off-broadway shows for free.
I’m a big music fan and there are always excellent concerts that are free or don’t cost a fortune.
And grocery stores - there are six grocery stores within a five block radius of my apartment and with covid going on if one didn’t have something then one of the others would, even if it looked like it fell off the back of a truck 
We got memberships to the Met and American Museum of Natural History for a year each. The AMNH was the better deal because students could get into the Met for free, I found out later.
In my experience pretty much every city with 50k or more people has a university in it. I’m sure there are exceptions but thats been my experience. Really most of the things you list exist in cities with 50k or more citizens. What seems to separate the bigger cities is the diversity and quantity of them.
Having personally spent time in a city of 1 million, 3 million and 8 million, for the most part all 3 have the things you expect a big city to have. However public transit tends to be garbage in the US outside of the large cities on the east coast and Chicago. Los Angeles is a huge city but their public transit supposedly sucks (I’ve never been there).
I remember taking a bus tour in China, out of Shanghai. As the bus rolled down the road, we passed a “town” and the tour guide said, “We are now passing by XXXXX, very small town, less than one million people.”
There are universities, and then there are universities… Plenty of cities/towns have institutions of higher learning. But there’s a HUGE difference in impact on the community between say… a 3000 student small liberal arts college, and a 25,000 student major research university.
That’s also the same basic distinction between a small city and a big city. Smaller cities may have the same basic stuff that larger ones do, but either have only one, or have a less capable/opulent/functional version.
And another thing that large cities have is specialization. Here in Dallas for example, we tend to have multiple tiers of everything- if I want liquor, I can go to one of dozens of really cheap places with limited selection aimed at lower income/price sensitive customers, I can go to the mid-range liquor supermarkets(Spec’s, Total Wine, Sigel’s and Goody Goody), or I can go to Pogo’s, which caters to connoisseurs. Most smaller cities may not have that level of specialization.
Big cities also have specialized businesses- food, beer, custom lingerie shops, etc… that smaller cities don’t necessarily have. And if they do, they only have one.
I do agree that there’s probably a certain critical mass size above which cities don’t really get additional sorts of amenities, just more of the same. But I’m not sure exactly where that line is- somewhere around 1 million, I’d guess?