Clearly the fault was not with anything in your home or anything you did.
Therefore I would suggest that you pursue Telstra
for a credit for the seven days
to get an explanation as to why your modem didn’t switch to mobile 4G so that next time there is a problem it works.
to get an explanation of why the tech could not log in or see what the problem was &
to assure yourself that MediAlert will work over your NBN
I agree with @PhilT that many alarm and alert systems which worked over landlines do not work with NBN. I may be necessary for you to change to a system that works over the 4G mobile phone system. (We have a Live Life Alarms 4GX that works well sending out a message we programmed in, to a chain of phone numbers we programmed in.)
Telstra did ask for me to contact them to make sure all was OK, offered to keep case open 2 days extra for me to test, I was offered a $15.00 off next bill, see what happens. Our MediAlert is the one where if Red panic button is pressed it rings 3 family/friends before ringing 000, so far haven’t needed to use it yet.
I checked the settings in my Telstra Modem, found Remote Access Box was unticked, couldn’t talk to anyone to see if this was login problem.
A survey is on its way which is where I’ll ask about the 4g switching problem.
When we lost our email but still had internet, I ran Speedtest and got our normal around 20Mbps down with 0.02Mbps up, now I get 76Mbps down and 6.3 Mbps up, can’t complain about that although I didn’t know Fixed Wireless went that high.