Bit of inconsistent behaviour I noticed. We have restricted the creation of new Office 365 Groups via an Azure AD setting, so only a specific group is allowed to created new Unified Groups (as per https://docs.microsoft.com/en-us/office365/admin/create-groups/manage-creation-of-groups?view=o365-worldwide).
Where the ability to create new UG's is surfaced across the office apps, for example in Outlook ('New Group'), in Teams ('Join or Create a Team'), or in Planner ('New Plan'), users not in said group receive an error message "Your organization's global admin has turned off the ability to create new Plans and Office 365 Groups" which is as documented.
Therefore users who are prevented from creating new UG's by this Azure AD setting cannot create new plans within an existing group, since that requires first clicking on the 'New Plan' button (which immediately throws the mentioned error) followed by clicking on 'Add to an existing Office 365 Group'. They can however still add plans to existing groups via the Teams UI (new tab in any channel > Planner app> create a new plan).
On a separate but related note, I noticed that when UG's are created via the admin portal, or by New-UnifiedGroup (as we routinely do in order to enforce our internal management standards upon them), the user who creates them is added as a group owner, but not as a group member. I thought the latter would be implied by the former (as the Teams UI suggests when managing Team membership - each user is listed as one or the other; never both), but it seems not. If you are not a member in addition to being an owner, you will be unable to see the group under 'All plans' in the Planner UI, and you will be unable to add new plans to the group via the Teams UI as above.