Hello Hvnly,
I'm Shalom and I'd happily help you with your question. In this forum, we are Microsoft consumers just like yourself.
Let me provide you with precise instructions on how to add your Hotmail account to your iPhone 15 Pro Max:
Unlock your iPhone and go to the Settings app. Scroll down and tap on “Accounts & Passwords.” Next, tap on “Add Account.” Choose “Outlook.com” from the list of options. Enter your Hotmail email address and your password associated with the account. Tap “Next.” Wait for your iPhone to verify your account information. Finally, choose the data you want to sync with your iPhone. And that’s it! Your Hotmail account should now be set up on your iPhone 15 Pro Max.
Best Regards, Shalom