Updating your password to access your email from a web page if using an email that needs an app password means you have to create a new app password

Some of the major email providers like, gmail, yahoo, aol, att require a separate password (app password) from the password you use to access your email from their websites, if you need to reset or update your password for their website (like gmail.com, or yahoo mail) it as shown below voids your app password. so short answer is if you need to change your email password, you will also need to create a new app password that can be used in TSS to allow you to email invoices to your customers.

Voided

App Passwords Removed After Changing Account Password

When you change your account password, all your App Passwords are voided. This means that any app that uses App Passwords will no longer have access to your account. You will need to create new App Passwords for those apps to regain access. It's important to note that this change is necessary to enhance the security of your account and prevent unauthorized access.

Microsoft