I'm not sure "standard" is accurate, I couldn't find any statistics on methodology for reducing and fixing fractures in long bones. But that's tangential, I just bring it up for general discussion if someone else finds data on that and would be so kind as to let me know since I'm curious.
But, fixation of bones via surgery goes back a few hundred years as an idea. Afaik, nobody knows who came up with the idea, but it was never viable until the late 1800s when surgeons started seriously working on it after Lister managed to figure out what caused infections.. The implements used weren't "off the rack", they were purpose made for the job in the hopes of preventing the known problems in implementation like the implants corroding or causing bad reactions.
From there, development of the implants was gradual, with changes to the acceptable design advancing as flaws were discovered and corrected.
The idea of internal fixation was pretty much accepted by the medical community from the beginning. I've never run across any formal opposition in the form of published opinion, but I'm also not a historian with access to the good libraries. My background in this stuff is hobbyist level interest with access to a decent medical library back in the nineties and oughts. That library wasn't for history, it was curated for doctors and focused on modern practice.
Anyway, the point of that was that by the time surgeons were doing procedures, the idea had already been long accepted, and Lister himself did some of the early work on internal fixation.
Now, some less search engine friendly stuff. There are examples of attempts at repairing bones via surgery going back to the bronze age. They were pretty badly done, iirc, and likely caused problems beyond that of normal surgical complications, but there are bones from archaeological digs that were wired or otherwise surgically altered with implants of some kind. Don't ask me for dates on that, I'm pulling the info from memory of articles I read over a decade ago, and I wasn't reading it for that kind of thing.
But, if you search up, use the term "internal fixation" and you'll get hits from medical journals, related publications, and likely some answers like this scattered among them. If you make it "history of internal fixation", I know there's several good histories of the subject online, I looked it up when my kid asked a similar set of questions when their grandmother had surgery a while back, to refresh what I had picked up back in the day.
Again, please remember that I'm pulling this from memory. Don't try and use it for homework or anything. It's accurate enough for this kind of use to give a general answer, but I can't recall any specific dates, and the only reason I remember Lister as being a huge factor is that he was a huge factor in everything medical. His name kinda sticks in your head when he's essentially the father of modern surgery as a whole.