Is it possible to get/train a carrier pigeon today?

I don’t know anything about it, so hopefully someone else has more experience, but I found this, so I assume the answer is yes.

https://pigeonpedia.com/how-to-train-a-carrier-pigeon/

Here in the Netherlands the “pigeon racing” sport is still relatively alive, but does have an aging target group. Pigeons are driven somewhere many miles anyway, (well km’s) and released, first home gets a price.

There are breeders and trainers etc.

if you’re really interested in pigeon behavior Rowan university in New Jersey has a pigeon lab for studying avian communication and cognition

Wikipedia has your back

So yes, they are still possible to train and use, are in active use (for example in photography for rafting), and there are RFC standards relating to internet over carrier pigeon. Also, they are actually favourable compared with ADSL so yeah, a legitimate possible option for some cases.

There's a homing pigeon club not far from where I live.

I once went down a rabbit hole looking at falconry. In my state its heavy regulated, it's probably the same with pigeons.

Since you've been obsessed with them lately, have you seen Who Is Cletis Tout? Great film that features some carrier pigeon action and an unconventional cast.

I was walking in the neighborhood recently and passed a guy putting a pigeon in a high up box in his yard. It was such a an odd thing that I wasn't sure what was going on, and mentioned to my daughter that I thought this guy was keeping pigeons, and she said "because you saw him KEEPING PIGEONS?" Which I guess is fair, it just was so weird I wasn't sure!

I don't know if he uses them to send messages, but some people certainly have them at least as pets.

No. They're extinct.