@Mahavir Saroj Thank you for posting your question on Microsoft Q&A platform. Happy to assist!
From the tile of the post, I understand that you want to migrate your on-premises Windows Server 2008 Rs to Azure and post migration upgrade it to Windows Server 2019. I see that you are aware that direct upgradation from Windows Server 2008 R2 to Windows Server 2019 is not possible as per MS documentation - https://learn.microsoft.com/en-us/azure/migrate/how-to-upgrade-windows
IMO, you can upgrade from Windows Server 2008 R2 to Windows Server 2012 post migration and then follow this approach - https://learn.microsoft.com/en-us/azure/virtual-machines/windows-in-place-upgrade#perform-in-place-upgrade-to-windows-server-2016-2019-or-2022 to upgrade from Windows Server 2012 to Windows Server 2019.
I'm checking with Azure Migrate team to get a confirmation on following the mentioned approach as a workaround to meet your requirement.
Thanks for your understanding!
Update:
Azure Migrate team confirmed that as of now there are no plans to support direct upgradation of OS (In you case - Windows Server 2008R2 to Windows Server 2019)
The current workaround would be to follow the approach mentioned in the screenshot below:
Hope this answers your question. Please reply if you have any further questions in this matter!
If the response helped, do "Accept Answer" and up-vote it