I'm curious what your sources are for this.
It's my understanding that the modern oud that most people play nowadays, particularly Turkish ouds, are rather smaller than those played in the late
19th and very early 20th century.
Surviving examples and literature suggest that ouds routinely used to be in the 63cm scale range and nowadays 58.5-61cm is more typical (and Turkish
ouds are all in the smaller end of this range). So contemporary ouds are already smaller than what you would likely have encountered in the late
19th century.
Women's ouds are not usually smaller in the scale of the oud, rather they typically have a shallower bowl to make it easier to hold. This generally
has a rather negative impact on the sound and projection of the oud.
From what I've understood, the oud has never been a particularly important instrument in Turkish/Ottoman music, it's more of an Arab instrument that
has been adopted (and modified to suit). Not sure if this has something to do with being associated with women, possibly specifically in Turkey.
I don't think such an association has been the case in Arab countries, or at least I've never heard that suggested. The oldest famous oud player
of course was Zeryab (a man) and he is practically synomous with oud.
https://oudmigrations.com is an excellent resource regarding historical ouds.
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