Hello AUZYP,
Thank you for posting to Microsoft Community. We are happy to assist you.
In order to understand your query and provide possible solution, May I please double confirm if you are using Microsoft 365 business email account or Microsoft Personal account such as Outlook.com, hotmail.com or live.com?
I have been testing your query from my side and based on my test result, if you are using Microsoft 365 business email account, you can able to add zoom add-in from the Outlook app store in the new outlook: To do this, Go to New mail -->Under Message, click on Apps -->Add Apps.

- Search Zoom add in from the search bar.

- Then add zoom for Outlook Extension add-in following the prompt steps. Once you finish set up Zoom, now you can create Zoom meeting from the new outlook.

Please note: if your Microsoft 365 business account is not primary in the new outlook, please kindly make it primary and try the above steps and check if there is any difference.
I look forward to your update. Please feel free to let me know how it goes or if I got you wrong. If you still have any concerns, please let me know so I can provide more suggestions.
Thank you for your precious time. Have a nice day.
Sincerely,
Community Moderator