Hi @Vanja Radunovic ,
Based on my research and test in my lab tenant, seems like adding shared mailbox as an additional mailbox is not yet supported in New Outlook.
Currently, to access a shared mailbox, a user with full access permission can add it by right clicking the left pane and choose "Add shared folder or mailbox":
This can make the shared mailbox show up in the "Shared with me" section:
However, regarding your need to set the shared mailbox as the default Send from account, I am afraid this is currently not feasible in New Outlook.
Given this, personally I'd recommend switching back to the classic version of Outlook for the time being and send a feedback via Help > Feedback:
Noticed that a post which mentions this feature has already posted to the official feedback portal for Outlook. I've added my vote there and you can also vote it up. Hopefully this can be realized in the future update:
https://feedbackportal.microsoft.com/feedback/idea/0c340c0b-9c15-ee11-a81c-000d3ae5b6f4
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