I've been put as an admin and I can't add products to my ID or install the software.
I don't know much about this, but I will note that being an admin doesn't grant you any free use of software. You still have to go through the licensing/purchasing process for yourself.
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By default, administrators don't have access to Creative Cloud. To get access, you must assign a product license to yourself and then install the apps.
To know more, please read the Admin guide -Assign a license to teams user
Let us know if this helps.