I'll always stand by this opinion but Bioshock Infinite
fucking sucks!
Only 1 & 2 are canon
and are the only true Bioshock games.
Infinite was just a straight-up downgrade in terms of worldbuilding, story, characters, and gameplay.
Columbia was a somewhat decent concept as a contrast to Rapture. It actually would have been a cool game to make a Bioshock spin-off around and I still remembered loving the pre-2013 previews. After all Columbia is essentially a Proto-Clerical Fascist American splinter and by contrast there's an organized Proto-Communist Guerilla Movement in which the two fight... While atop a floating city in the sky.
That sounds really cool!
Except they aren't actually that fascist and the intersection between the world and gameplay (practically a cornerstone of the previous games given how Rapture's lore was married perfectly with the gameplay) was just not there at all.
Why would an authoritarian state like Columbia allow weapon vending machines where anyone (including would-be rebels) buy a gun? Every authoritarian regime in history was
never friendly to gun rights. You'd at most be allowed to own a shitty hunting rifle or shotgun and guess what, Columbia doesn't have any wildlife to hunt.
Why the fuck does Columbia have super progressive rights for women in 1912 (50% of the Columbian Army you fight are women) but they're pretty much chuddy every other policy? This game was made well before DEI became mainstream (like Black Nazis in Battlefield 5) so it's strange how there's plenty of scenes establishing Columbia as being firmly racist yet not even following standard gender norms of 1912? I'm not asking for a rehash of the Handmaiden's Tale but it was legitimately immersion breaking that for a game set before WW1 they have ultra progressive (by 1912 standards) women's rights but pretty much 1850s-tier face relations.
Also how come they voluntarily grabbed a bunch of niggers and chinks as cheap labor and then bitch and moan about how they're starting to revolt? Did they not learn from the slave trade that bringing niggos for cheap labor is not a good idea at all?
How come they're super religious prudes but then they allow sexy demon lady designs on Vigor bottles? And actually why the fuck would they allow a product called
Devil's Kiss to be sold? Or Vigors for that matter? Religiously they're basically ultra-fundie WASPs with a personality cult around Comstock, they wouldn't allow anything that changes your God-given-body.

They're supposed to be more strict than 80s Christian soccer moms but then this is fine by them, lol.
All of the Bioshock gameplay hallmarks like the weapon vending machines and plasmids made since in 1&2 because Rapture was basically Ancapistan. In a more well designed game Booker would've been getting his gear from the Vox and/or raiding Columbian Army supplies. Still don't know how Vigors would make sense in Columbia unless it's smuggled in from an outside source.
Doesn't matter though since the
real focus of Infinite's lore is the shitty multiverse slop that basically ruins Bioshock 1/2 by retroactively making their worlds be heavily reliant on Ken Levine's Mary Sue OC. I'm sure we all remembered when the Burial At Sea DLC basically screamed at the viewer: "IF IT WEREN'T FOR MY MARY SUE ELIZABETH, YOU WOULDN'T HAVE BIOSHOCK 1! EAT THAT YOU FUCKING CHUDS!" and all that people Infinite for is the porn for said OC, lol.
Also the gameplay was just shit. Two weapon limit, do I even need to say more? It did even help they refused to try to make the guns somewhat themed around the year of 1912.
Again Bioshock 1/2 had Rapture which was basically culturally frozen in the 1930s since that was the time the city was built and construction was hastened by 1945 after the nuclear bomb was revealed and Ryan had a schizo meltdown over how the world was already going to end (it did not). Hence why Tommy Guns, pump action shotguns, etc. were the norm. Alongside a lot of unique guns that could only exist via innovations by innovators unrestrained from government bureaucracy such as the Chemical Thrower and Spear Gun for example.
In Infinite you basically main the generic assault rifle and RPG for the rest of the game. It would've at least been interesting to see what if you had to rely on old bolt action rifles or something, pre-WW1 style.