InitiateAuth command and 50 000 MAU free tier

[isRostCompany]

Hello.

Planning to add Cognito as an identity provider to my application.
One of the requirements for user log in is to be able to track when users log in, how long their session
lasts before log out, etc.

So it seems that I cannot just call Cognito log in from web browser, but instead would need to utilize the
solution from
https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-identity-provider_example_cognito-identity-provider_InitiateAuth_section.html
in my app.

And so my question is: does this way of authenticating users (using login/password pairs, but through centralized webserver) still falls under the 50 000 MAU free tier, or is it considered something else?