But there is no L8 prod manager job at Amazon that I am aware of. L7 is principal and L8 is a manager. And there is no L9 at all. If you want to be L8 you need to be looking at Dir / GM roles.
L8 at Amazon is director level. On the retail side… get ready to spend 10-15 years to get L8. Much more achievable to climb to L8 and beyond at AWS. There is no L9 role at Amazon. Basically everything you said :)
I will add you can be an L7 manager of prod management or an L7 principal IC. Different career paths
If you’re an L7 at Google you should shoot for high L8/ L9 at Amazon. Amazon uplevels across their PM org, and pays are lower than market very often