@Mohamed Achraf Chourabi Greetings!
As per support matrix - https://learn.microsoft.com/en-us/azure/site-recovery/concepts-trusted-vm#support-matrix only Windows OS is supported and there is no update yet on Linux OS support. We will check with the product team if it is on the roadmap and update this thread if I hear back from them.
Thanks for your understanding!
Update: Azure Site Recovery product team has announced "Private Preview: Azure Site Recovery support for Azure Trusted Launch VMs (Linux OS)" To enroll in the private preview, please share your interest by filling up the enrollment form.
Hope this helps!
If the response helped, do "Accept Answer" and up-vote it