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I have similar situation and have used this answer Send data from Lightning Web Component (LWC) to a Visualforce page from @salesforce-sas which worked perfectly for me.
Now I have the problem in the other direction - that is sending data through an event from VF Page -> Aura App -> LWC.
I see some ideas on this but nothing that solves this specific issue. Any help would be appreciated.
You can now use Lightning Message Service for communication across VF page, lightning and LWC.
Try with example mentioned in release notes
https://releasenotes.docs.salesforce.com/en-us/winter20/release-notes/rn_lc_message_channel.htm
