Torey_Kieson Thanks for the comment. As described on the article, when it comes to provisioning, the mailbox can take up to 24 hours (especially on hybrid scenarios where we also have the Entra Connect time between syncs element). You may be experiencing a different behavior when you provision the account directly in Exchange Online, but just like on when creating a remote mailbox and having Exchange Online provisioning it, there might be times where even on that scenario it can take up to 24 hours and might not be instant. All in all, except for the time between syncs in Entra Connect, the provisioning behavior can take up to 24 hours regardless of how you provision the mailbox. (Trust me, I've seen both taking some time :))
Regarding the ability to manage groups created in on-premises from a mailbox hosted in Exchange Online. Nothing I can share about it, sorry for that. For the time being, I would recommend as a solution to re-create the groups in Exchange Online and replace it in on-premises with a MailContact.