How do switch my Apple ID profile to an existing profile?

By "profile" do you mean Apple account/ID?

Merging Apple Accounts or transferring data is not officially supported, nor can it be done easily or completely.

Apr. 2018 post by ASC helper Winston Churchill on transferring data from one Apple ID to another. https://discussions.apple.com/message/33333380#message33333380

Feb. 2021 tips from Eric Root https://discussions.apple.com/thread/252468781?answerId=254653802022#254653802022

Look into using Family Sharing to continue to be able to use items purchased with one Apple ID with other Apple IDs.

Family Sharing - https://support.apple.com/HT201060

Set up Family Sharing - https://support.apple.com/HT201088

Fortunately when you sign out of one ID and sign in with a different one it asks you in most cases if you wish to retain the data from it on your device. Say yes and then delete individual items you do not want.

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> https://support.apple.com/HT208242

If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.

Click on this link to learn how to 'Sign in with your Apple ID' --> https://support.apple.com/HT204053

I am still not clear as to exactly what you are asking. if you mean signing in with a different account:

On your device sign out of the old account if necessary; sign in with the new one.

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> https://support.apple.com/HT208242

If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.

Click on this link to learn how to 'Sign in with your Apple ID' --> https://support.apple.com/HT204053