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It's long and boring, but basically, if the cookie path is a prefix of the request path, and the cookie path ends with "/" then it will work. So for you, there is a specific order of operations where the cookie consent will work from site A to site B, but not from site B to site A.
Let me explain that first with the settings for your site to make A to B work. Site A would be your primary domain, not the subdirectory. Joomla Global Configuration would need these settings for the cookie domain and path:
Now, if a user arrives at your main site (learn-greek-online.com) and accepts cookies, the consent would be valid at learn-greek-online.com/ask-greek/ - this is because the cookie path "/" is a prefix of "/ask-greek/" and it end with a "/" - meaning it is valid for all subdirectories.
If a user arrived at "/ask-greek/" and accepted cookies, however, that consent would not be valid at "/"
Now, here's where it gets interesting, and also maybe cause some issues. If on the "/ask-greek/" site, you set the cookie domain and path identical to the main site, it might work in both directions. A-B and B-A - but I've never tried it. It might cause errors for any user who logs into one, then visits the other - session cookies wouldn't match and might cause errors - again, I've never tried such a thing.
It's super late, so not something I'm ready to test tonight, but it would make for a good experiment.