Well that heading was quite a mouth full. I came across the issue below earlier today when adding a plan to Teams, this seems to be an issue primarily for Teams/site owners.
The issue presents as in the image below when a user navigates to a Planner instance that they don’t have access to –
To view or edit this plan, including any task in it, ask any member to add you to the Members list of this plan
This is caused by a user being an Owner of a group but not a member, Tasks/Planner only appears to synchronise membership permissions rather than Owner permissions and so Owners aren’t granted access. In my mind this is an obvious design flaw however others do seem to disagree – https://techcommunity.microsoft.com/t5/planner/team-group-owner-has-to-be-a-member-as-well-to-access-planner/m-p/338355
The solution is quite simple luckily, ensure that any owners of Teams are also added as members to the relevant SharePoint group.