Hello Giulio Acconciaioco,
Greetings!
Thank you for posting on Microsoft Community!
I understand that your Outlook signature frequently disappear after the latest update for Microsoft 365 apps.
Could you please kindly share the current version number of your Outlook to us? What version of Outlook do I have? (Please mask any private information)
As you also mentioned you are using New Outlook, I'd advise you to revert back to the Legacy Outlook by switching the toggle off in the New Outlook and it will automatically open the classic version. Please comprehend that the New Outlook is a beta version, and the product group are collecting feedback from customers to develop the product better.

And if your Outlook version is on Current Channel, this issue may be caused by roaming signature feature added by Microsoft. Since Outlook previously lacked signature roaming functionality, some users may encounter signature sync issues after the update. You may create a registry entry to prevent migration of signatures and disable the feature as a workaround:
Path: HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Outlook\Setup\
DWORD: DisableRoamingSignatures
Value: 1
This is a DWORD value, and setting it to 1 will disable the feature and prevent signature migration upon rollout. Device administrators can choose to use its corresponding Group Policy location to the same effect:
Path: HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\Office\16.0\Outlook\Setup
DWORD: DisableRoamingSignatures
Value: 1
Refer to Outlook roaming signatures
If you need further assistance, feel free to reply. We will continue to support you!
Wish you have a nice day!