Some of this depends on where. In US waters under GC control, it's easy to expect more, and on liveaboards that are more than an hour or two from port much of this becomes more important. To try to answer in general terms...
O2 kit with plenty of O2 to get back to shore - more than enough please!
PLB and
AED links added - but wishful thinking.
Realtime CO monitor - I wish
handheld CO tester - I wish, and even if they do, how do we know they calibrate regularly and correctly? I carry one now.
O2 analyzer - I've seen some provided I didn't want to use. I bring my own.
Basic first aid kit - at least
Advanced trauma kit - on liveaboards
EMT or Paramedic, Nurse, Physician - expensive thinking
Chase boat - for liveaboards
Crew left onboard while passengers are diving - always
More than one crewmember left onboard while passengers are diving - depends
Suited safety diver or Suited rescue swimmer- for liveaboards
Sat phone - for liveaboards
Deco bar/safety stop bar - get a bigger tank; carry your pony or deco bottel
Underwater O2 delivery for "emergency deco" - dive responsibly
Recent (or any) air test results - I gave up
What else do you consider essential safety gear that the boat needs to provide? How many of you check that the boat actually has any of this gear before you book. - I gave up. Even if you get answers, you can't depend on them
"I have NEVER been asked for the results of my air test. By anyone." I started to but didn't for a couple of reasons...
My other experiences in asking to see had been futile, and I still dived those tanks. I was still struggling with that issue at the time - and there was a side issue that trip I didn't mention.
I was so impressed with your command, boat, and crew - I decided it would be silly for me to second guess you on anything.
I no longer trust quarterly tests. I dived tanks that passed with flying colors right after filter changes, but last month were testing 5 ppm CO. I'll test my own now.
But thanks for asking...
Radio, fire extenguisher and life raft.
I once had a boat try to take me across the Roatan-Utila channel without life vests or extinguisher. I took PFDs, and now carry an inflatable one of my own - often wearing it. Fortunately he had a radio when his transmission failed. I've been at two emergencies that either the O2 failed or they ran out.
I do tend to evaluate a boat & skipper more than ever, especially outside of US waters - but usually try to protect myself as much as possible. If I die in foreign waters in spite of my efforts, I've discussed this with family already.