Food injector syringe ???

That is a serious piece of equipment. Yes I have injected hams, turkeys,chickens. It does make it more juicy and does improve moisture, and flavor. Try it and experiment with flavors. No I do not have that serious injector model, just cheap model from wally world.
I have two like that. I use them to inject pork butts, pork and beef loins, chickens, and turkeys. For turkey, I buy the cheapest store brand and pump it full of a mostly butter concoction with some seasonings in it, making my own version of a Butterball.
BUTTER !!!!!!

Ahh, this is still one of my "maybe someday" projects to recreate..

The short version is he replaced all of the bones with hollow tubing and pumped 150F butter through them to cook the turkey... then later drizzled hot oil over the skin to crisp it.

On the original topic, I have one, maybe two.. they came as part of some other kit I believe. I rarely use them though but probably should.

A semi-related technique I do like is "larding" where you stab a knife in a roast and then pull... various things through it. Traditionally the things used to lard the meat would be fat (aka strips of fatback or bacon) but I've also enjoyed carrots and garlic. Works best when done with the grain so when you cut it cross grain you get delicious little rounds of flavor sliced out.