There's a lot to unpack here. As a newly certified diver, I imagine you were taught you and your dive buddy were to execute a formal buddy check of each other, likely aided by a mnemonic, prior to every dive. This was obvious, detailed and took some time. Then you got on an actual dive boat and didn't see any of that, and you're wondering what's 'normal,' what to expect and how to deal with it. Good questions!
I didn’t get to set up my own gear as the instructor who was on the dive rushed in and took over for me as he wanted to get going.
It's a good idea to go over the setup of your own gear; pay attention to whether the regulator is attached to the tank and the air turned on, is the low pressure inflator hose hooked to your BCD so you can inflate, what's the starting tank pressure, etc... Sometimes watching someone else set your gear up (a service often offered and sometimes the default on dive boats; many people appreciate it, but you'll see plenty of posts on the forum deriding it) is okay, but it's your gear, your life, take that second look.
Once out there, it was just a flurry of activity in the boat and I didn’t see any safety checks.
Yes, and don't hold your breath expecting them. Over time some people get complacent, but also more independent and able to 'run the check' in their minds without pointing, saying things, etc...
If you watch me pre-dive, you see me pointing at each main piece of gear in turn while muttering, make an 'OK' sign, then do it again. I may do something similar before exiting the boat with gear...since I once left an expensive set of fins on a dive boat.
He set mine up so he knew it was ok but I could only verbally ask him about his
It's good to take mental note of others' setups, but don't expect everyone you meet to be 'drilled' by you. There are some less common gear configurations you would be aware of as you may encounter them. And Air2 ditches the standard octopus and builds one into the power inflator coming off the BCD. Some people use a 'long hose,' and in out-of-air situations donate their primary reg. and breath off their secondary, if I understand correctly. And a backplate/wing looks a little different from a standard BCD.
I don’t know if other people did theirs on land or what have you.
Unless you are diving with someone really new who you fear will get into trouble (and drag you into it with him), you may be best served with the old adage 'Live and let life.' Some people do it in their heads. Some may not do it at all.
I eventually was also paired with a different diver as the instructor had to help a refresher student. No checks happened.
It's worth noting you can quickly relay and ask about a couple of things without the whole checklist. I might mention I've got an octopus, and gesture at it, and my weights are integrated (I usually don't wear a weight belt, but may). I look at the other diver's rig to see if he's got an Air 2 or uses a weight belt.
For a new diver to be rushed like you were probably isn't rare, but it's not ideal.
Another issue; modern mainstream OW coursework tends to indoctrinate an interdependent 'buddy system' style of diving. The farther out people get from that training, the more independent some grow. Many people don't have a consistent 'travel buddy,' and don't like relying on the inherent unknown of an instabuddy. Some of us have taken a solo diver course (or other coursework instilling independence), and we approach dives feeling responsible to monitor ourselves. That's why I sit there pointing and muttering like I'm nuts. I have a ritualized internal checklist.
You're facing one of the first 'challenges' of certified diving from boats; the boat milieu often appears much different from what you learned in class. But this is cause to be more mindful and more careful...not complacent and sloppy.