Hello Mateusz Janusek,
Thanks for your post here.
According to the screenshot you provided, my understanding is that you can't enable Outlook Web App for your mailbox. Given this situation, you can try another method to enable it. To do that, please click Exchange in the left pane of Microsoft 365 admin center to go to Exchange admin center, then click recipients > mailboxes and double click on your account, then select mailbox features and then enable Outlook on the web or others like to following screenshot:
If you need further assistance, please kindly provide the following information to me and I will try my best to help you:
1. If there exist other administrators in your organization, please double check whether other administrators encounter the same issue.
2. If you manage email apps for other users, will you get the same error message?
Thanks for your time.
Regards,
Seven