Re... "Then doing so, you may see the date with the options listed while typing your search criteria."
FWIW - I've tested this pretty throughly.
In both iOS17 and macOS Sonoma, while you can technically search "by date" (ie 10/2) such a search will only return photos that contains text "10" and "2" but will NOT return photos taken on 10/2 or October 2.
While users can still search by MONTH or YEAR, by DATE is no longer available and appears to have been intentionally removed in iOS17 and macOS Sonoma.
The only way to get that functionality back at this time is to restore to the prior OS.
I have put a feature request into Apple support but do not expect that this will be resolved - which is a bummer for those of us that used that functionality regularly.
Hope that's helpful.