You might have more than one account, try switching on the left.
Add the product through the ‘My Members’ section on the left (Modify product access)
see if it helps. If you do not see any members, you need to add it, first.
Normally, when purchasing, there is a checkbox to automatically assign the product to the enduser.
I have followed the step you said until the modify product access. But I cannot click on the checkbox for SketchUp Shop.
Do you use the Google sign in, below or the yellow Trimble? Try signing out and back in using the Trimble one, you might need to update your password.
better use this form:
I had filled up this form already and get a reply through email. But my problem is still not fixed yet. Then, I email my problem again to SketchUp team with uploading my payment history and plan settings photo, and not getting any reply yet.