I have a unique situation I guess. I have a EXCH2016 hybrid with a few mailboxes on premises and most in O365. Free/busy works fine both directions. but now we acquired multiple companies, each in O365 (no hybrid). We configured org relationsships and they can see on prem free/busy ok, but can't see hybrid cloud user's availability. If they manually test using the onmicrosoft.com, it also works. OWA logs from external party show:
"Autodiscover failed for email address jdoe@xxxcorp.mail.onmicrosoft.com with error System.Web.Services.Protocols.SoapHeaderException: An error occurred when verifying security for the message."
So, on prem is redirecting autodiscover as expected.
This tested ok a year ago. The only change was we got rid of EXCH2010 and reran the HCW to enable OAuth. It has been suggested to disable oauth again, but I don't want to.