Hi ChorizoBurgler,
I have just checked on my side, and the issue doesn’t appear. To check whether the issue is related to Teams client or other factors, please go to
Teams Web App to take a check and view whether Planner can be open there.

In addition, for better using experience, we recommend you update Microsoft Teams to be latest, click Profile image > Check for Updates.
If issue persists, please offer me more details for further analysis.
- Screenshot of the problem.
- Is your organization set certain conditional access policy? If so, you may check whether it will affect Teams to access Planner.
- Whether other members in your organization have the same issue.
- If you change a more stable network, is the situation better?
Regards,
Betty