Migration from Gmail to Infomaniak

After some research I found Infomaniak as maybe the best solution space/price as substitute to Gmail and Google Drive. The migration is quite easy for email specially, it's possible to import all by previous emails from Gmail and redirect new ones.

My question/ doubt is now what happens to my google account. I have an Android phone, so it's almost necessary to keep the account because of that, I also have to keep the gmail at least for a period of emails to be redirect and gives me time to change all subsctrions to the new email, warn my contacts, etc.

During this period google will continue to use my data, no? What can I do? After complete migration I plan to deleted everything from the drive and all emails, but I have no clue if that's enough.