Here is an evaluation of injuries vs, turf type for the US NFL.
https://www.footballoutsiders.com/stat-analysis/2017/turf-type-and-nfl-injuries-part-I
https://www.footballoutsiders.com/stat-analysis/2017/turf-type-and-nfl-injuries-part-ii
The types of injuries are the same as in "soccer"- knee (ACL, MCL etc) and foot/ankle etc.
The artificial surfaces result in about 50% more injuries than natural grass. There's a pretty wide variation depending on the exact nature of the artificial surface and the quality of the upkeep, whether artificial or grass, but the numbers are seemingly pretty compelling.
However, the conclusion in Europe, as of 2006, was different,
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2577464/
More up to date info. on professional football (soccer) is hard to come by, for some reason, so here is one on amateurs.
https://bmcsportsscimedrehabil.biomedcentral.com/articles/10.1186/1758-2555-3-3
This concluded that artificial surfaces had fewer injuries than dirt fields.
Then there was this meta-analysis of a number of studies,
https://www.hindawi.com/journals/jsm/2013/380523/
This also concluded that for soccer artificial surfaces were less likely to result in injury.
By the way, I live in the US- North Carolina- and I've been a long distance Rangers supporter since I was a wee lad raised in East Belfast.
To my shame, I've never been to a game in Glasgow as I left N. Ireland as a teenager, but I track them and watch the games on video when I can.
If Rangers make it to Baku I intend to go as I have an associate that came from there during the time of the Soviet Union and he's encouraging me to take the opportunity.