Modern HCW (Hybrid Agent): troubleshooting like a pro

fatshark_2k , sorry for delay.

Strictly speaking from Hybrid Agent perspective, Autodiscover record is not required externally. However, other workloads requires it. For example, External Outlook client requires it, HMA or Teams accessing on-premises mailbox calendar.

Regarding the requirement to point Autodiscover to on-premises CAS it is valid as long as there are on-premises mailboxes with that primary smtp address domain or on-premises public folders configured for hybrid access.

Some references here:
https://docs.microsoft.com/en-us/exchange/hybrid-deployment/hybrid-agent#constraints 
https://docs.microsoft.com/en-us/exchange/hybrid-configuration-wizard-options 

https://docs.microsoft.com/en-us/exchange/decommission-on-premises-exchange#scenario-one

As far as all internal URLs yes they would need to be populated and discoverable within the Exchange On-premises environment.

Does the HCW agent use the internal EWS URL for the AAD proxy connector internal URL?
Documented here: https://docs.microsoft.com/en-us/Exchange/hybrid-deployment/hybrid-agent#constraints 
The Hybrid Agent registers the internal fully qualified domain name (FQDN) of the CAS server selected when running Hybrid Configuration wizard in the Azure Hybrid proxy infrastructure. If the registered CAS is offline, free/busy look ups from your tenant to on-premises and mailbox migrations to/from your tenant won't work. If the selected CAS is permanently offline, a new CAS server must be registered. Run the Hybrid Configuration wizard again to register a new CAS server. You can also point the internalURL on the Hybrid application to a load balancer instead of CAS: https://docs.microsoft.com/en-us/exchange/hybrid-deployment/hybrid-agent#direct-your-hybrid-agents-to-the-load-balancer-instead-of-a-specific-server