I don't know how fruitful it is to attempt to determine the extent to which the respect for knowledge then prevalent was a result of Islam or of other factors. The simple fact is that for a period that covered at least the physician's life, preservation and extension of knowledge was prized in that area.
Contrast that with the predominantly Christian cultures to the northwest-ish, that were at that time far more concerned with dogma, their own intellectual flourishing still a few centuries. What we in the west know of the ancient Greeks we owe to the Arabs, who were predominantly muslims, of that period.
It's far more complicated than that, of course, but to this day, writers conflate "Islamic" and "Arabic" when referring to that period (cf, e.g., [1]), and I think forgivably so. I think.
(I hesitate because on the one hand it is both difficult and fraught to tease apart the various influences, on the other hand western society was predominantly Christian and many of the western values I cherish arose and flourished in those Christian societies, on the third hand there was definitely a Jewish influence in some of those societies and an Islamic in other, on the fourth hand I share many of those values despite being none of Christian, Jewish, or anything else theistic, and on the fifth I am often irked when Christians claim (wish I could find a source, but alas, I cannot, but I've seen this many times) that those values could NOT have arisen elsewhere... not enough hands to balance these complexities.)
[1] https://greekreporter.com/2022/09/01/how-scholars-islamic-go...
(I am often reminded of how applicable to social discourse is Postel's Law, written in regard to TCP, "be conservative in what you send, be liberal in what you accept" - be liberal, be open in one's interpretation of the wording of others, seek neither offence nor exclusion when one can charitably and gracefully assume none was meant. Nope, he didn't mean it that, but it does seem a useful heuristic.)