Fully Migrating Exchange Server 2019 to O365

Generally it's recommended to keep the on-prem server if you are using it for relaying because it's required for managing on-premises attribute values (remember that you are syncing accounts from on-prem to O365, so most attribute management needs to be done on-premises). There are restrictions about relaying directly to EXO (You can see details on this here), and you need to ask yourself how comfortable your admin/support teams are with using PowerShell to manage Exchange attributes, as this is the only supported option available to you if you decommission your on-prem Exchange server. Details on some restrictions can be found in this document