Not sure what the difference is between an admin role, compared to the server administrator and organization administrator roles. Could not find more clarification on this, from what I can tell, I should be able to install plug-ins.
If you are still facing this issue here is the way I solved it.
You have to change the configuration of a Grafana workspace using the Amazon Managed Grafana console.
Open the Amazon Managed Grafana console.
In the left navigation pane, choose the menu icon.
Choose All workspaces.
Choose the name of the workspace that you want to configure. This opens the details for that workspace.
Choose the Workspace configuration options tab to see the instance configuration options for your instance.
Select Edit next to either Grafana alerting or Plugin management.
Plugin managementTo turn on plugin management, select the check box to Turn plugin management on. Turning plugin management on allows admins in your Amazon Managed Grafana workspace to install, update, or remove plugins using the Grafana plugin catalog. This option is only available for workspaces that support Grafana version 9 or newer.
After this when you login:
Logged in as the Admin role.
Configuration > Plug-ins > Search for Plugin
The Install button for the plugin becomes visible. I hope this helps.