Access to Plans within Microsoft Planner are tied to Microsoft 365 Groups. This means in order to share access, you add people to the group not directly to the plan. The easiest way to do this is via Outlook, although the same settings can also be accessed from Planner.
Open Outlook (in bowser or desktop app)
In the left-hand menu, click Groups – if you don’t see Groups, first click the grid (App launcher) icon then Groups

Select the Group that is linked to your Planner plan from the list, and on the right click the People / Share icon

Add those people you are sharing with and confirm – these new group members will automatically have access to the Planner plan associated with this group
This method takes you to the same settings, starting from Planner instead of Outlook:
Open Microsoft Planner and select the relevant plan
On the right-hand side, click the People / Share icon
In the modal, click the arrow next to the group name

This will open the group in Outlook, where you can add members as described above