Prevent Safari Auto-sign in

To force Safari to prompt you for a specific Google account every time on your Mac and iPhone, you must clear the "remembered" session data that Google stores in your browser's cookies.

On Mac (Safari)

Safari does not have a native "Multiple Profiles" feature like Chrome, so you must manually clear the session or use Private windows. 

Sign Out and Remove: Go to google.com, click your profile icon, and select Sign out of all accounts.

Clear the List: Click "Remove an account" and delete each account from the list. This forces Google to ask for your email address next time rather than just a password.

Prevent Auto-Login: Safari may try to automatically log you in using saved passwords. To stop this:

Go to Safari > Settings > Passwords.

Uncheck "AutoFill user names and passwords".

Use Private Browsing: If you want to access a specific account without it "sticking" for your next session, open a New Private Window (Command + Shift + N). 

On iPhone (Safari)

Sign Out: Go to google.com in Safari, tap your profile icon, and select Sign out of all accounts.

Clear Browsing Data: To ensure no "hidden" tokens are kept, go to Settings > Safari > Clear History and Website Data.

Note: This will sign you out of most other websites as well.

Turn Off AutoFill: Go to Settings > Passwords > Password Options and toggle off AutoFill Passwords and Passkeys. This prevents Safari from instantly filling in your "primary" account details.

Private Mode: Like the Mac, using Private Browsing mode in Safari (tap the tabs icon > [Number] Tabs > Private) will force a fresh login every time you close the tab. 

Stop "Sign in with Google" Pop-ups 

To stop the annoying prompts asking you to sign in while browsing other sites:

Go to your Google Account Security settings.

Under "Your connections to third-party apps & services," click See all connections and then the Settings gear.

Toggle off "Google Account sign-in prompts".