@Jean118 your place is stunning!
Re: Carpets. May I suggest you close the place up when you have a period of days to do so then observe if the mustiness emerges. Thereafter wrap up in plastic wrapping all the carpets and put into a space at some distance such as a garage. Air your property again and after hoovering see if you obtain relief.
If you then return each carpet one by one you might be able to detect the worst offender... if not all of them ....although regrettably it is most likely to be all if them. But prove it to yourself if any can be tolerated by re-introducing one at a time.
These look like valuable heirlooms. Could you sell to someone with the specialist cleaning and renovation knowledge??? possibly worth more than the carpets currently.???
I do hope the above suggestion is of help and that it doesn't in any way cause offence or disappointment. As you might gather I've had personal experience of heirloom carpets xxxxxxxxxx