Antibiotics generally are all post-WWII, except sulfa, so what was really changing outcomes from wounds was non-antibiotic antimicrobials. Not splitting hairs here; the difference is significant. Already by the turn of the 19th-20th century, it was known that silver, for example, held profound antibacterial properties. Ehrlich's "Salvarsan", a combination of arsenic with organic compound, was considered a 'magic bullet' against syphilis by the first decade of the 20th century. And it was Henry Drysdale Dakin, working at a field hospital in France during WWI, that would forever change the science of wound care. Working in conjuncdtion with Alexis Carrel, a Nobel Prize-winning French surgeon, he found that a dilute sodium bichlorite solution (think Chlorox plus Alka-Seltzer) had dramatic, and I mean dramatic, bacteriocidal power, and by using a dilute form, he was able to avoid the injury of healthy tissue in the area around the wound (that problem had proved insurmountable in earlier efforts in the late 19th century using solutions like full-strength chlorox, which proved toxic to tissues).

Against the protestations of fellow surgeons of the multinational allied forces of the U.S., France, Great Britain and others, Dakin argued roundly against automatic amputation of open fractures (gunshots or explosions that produced bone fracture), and to the amazement of all (likely including Dakin himself!), he proved that one could heal an open fracture without infection, by keeping it soaked in "Dakin's solution." In 2022, Dakin's solution continues to be a mainstay in the most grossly-contaminated wounds (think gangrene and bed-sores) in terms of initiating healing and controlling odors (I think one would vastly prefer treating patients in an environment that smells of a commercial laundry, rather than a meat-packing dumpster).

So yes, credit Henry Dakin with the dramatic improvement in wound care during WWI and right up to today.

Prior to WWI, and dating back to the 'Crusades Era' to which you refer, there was known to be antiseptic (no one knew about the role of bacteria and fungi in infection prior to the 1870's or so), the other solution which demonstrated efficacy over and over again, was vinegar. There is a variant second verse to the old "Jack and Jill nursery rhyme, dating back at least to the late medieval period, that goes "Up Jack got and off did trot, as fast as he could caper, to Old Dame Trot, who patched his knot with vinegar and brown paper." [The "Old Dame Trot" reference is also of signficance in dating this verse, but at the risk of chasing you down yet another rabbit hole, I will simply direct you to google Trota of Salerno and read what you like]. At any rate, by the end of the medieval period, dilute vinegar was noted to have antiseptic properties in wounds, while again not producing dangerous damage to normal tissues in the wound area.

So vinegar became a mainstay in wound therapy throughout the early modern era up into the 19th century. It too still enjoys some cachet in modern wound therapy, but has perhaps been superceded by dilute forms of Dakin's solution.

Finally, the use of honey in wounds, which is almost certainly prehistoric, also continues to this day. has a unique efficacy and cost-efficiency, which makes it useful right up to 2022 in wound healing. Now the honey used is not typically over-the-counter from the condiment section of your local grocery, but rather is a formulation known as "leptosperrmum honey" or commercially as MediHoney (still quite sweet and flavorful, but specific for wound care). It tends to stimulate the normal host inflammatory response in a wound, thus separating out necrotic tissue from normal tissue over the course of several days.

So, credit Henry Dakin for sure with the advances during the 20th century. Further advances now in the past twenty years in wound therapy have resulted in the capability of healing wounds that a generation ago would have been considered unhealable, to being resolved in less than 60 days.