To do what you are describing requires two components: the physical optical drive and the Blu-ray player software.
The first is easy. Just buy whatever suits your fancy/budget from Amazon, etc. Optical drives have been commodity components for well over a decade, it doesn't matter which brand you buy for mundane uses. There are only 2-3 manufacturers who are still producing the drive mechanisms, the guts are all the same.
The second requires a third-party payware Blu-ray player application. This will set you back about $30-50. Why? The price covers the license to the Blu-ray consortium (or whatever they're called) for playback. It's this license fee that caused Steve Jobs to called Blu-ray a "bag of hurt" back in 2008 and killed off any chance of Blu-ray drives being included in Mac hardware. It would have added $15-20 of extra cost to every single Mac with a Blu-ray drive which Steve didn't want.
I have a ten-year-old Slimline Blu-ray drive (the guts are Pioneer) that I've used on a variety of Macs over that timeframe. It is not a good user experience.
The physical drives are cheaply produced and tend to rattle, wheeze, and shudder much more loudly than a standard set-top Blu-ray A/V player. The software user interfaces are particularly clunky and don't integrate well.
Today, I just rip Blu-ray media with MakeMKV and transcode using Handbrake so I can view the content on a variety of devices. I still have a cheap standalone Sony Blu-ray player for basic playback of silver optical media (audio CDs, DVDs, Blu-rays, etc.). It's a lot quieter than the Pioneer Blu-ray computer drive.
So yes, you can watch Blu-rays on your MacBook Air with a Blu-ray drive and the requisite player software but it's not what I would call a pleasant experience.