How can I change the email that is inside the default email texts of wordpress?

There is definitely a filter for that!

Here is the reference link to wordpress developers page: https://developer.wordpress.org/reference/hooks/password_change_email/

Basically adding this function (with changes) to your functions.php will override your default password reset email.

apply_filters( 'password_change_email', array $pass_change_email, array $user, array $userdata )

full example:

add_filter( 'password_change_email', 'rt_change_password_mail_message', 10, 3 );

function rt_change_password_mail_message( $pass_change_mail, $user, $userdata ) {

 $new_message_txt = __( 'Hi [first_name] [last_name], 

 This notice confirms that your email was changed on on our site.

 If you did not change your email, please contact the Site Administrator on our site.

 This email has been sent to [user_email]

 Regards,
ME' );
 $pass_change_mail[ 'message' ] = $new_message_txt;
 return $pass_change_mail;

}

Checking the notes there, you’ll see that the message is part of the $pass_change_email array. SO if you just want to add something to it try this…

add_filter( 'password_change_email', 'rt_change_password_mail_message', 10, 3 );

function rt_change_password_mail_message( $pass_change_mail, $user, $userdata ) {

 $new_message_txt = __( 'new text with phone number' );
 $pass_change_mail[ 'message' ] = $pass_change_mail[ 'message' ] . $new_message_txt;
 return $pass_change_mail;

}