How to limit HA data usage to the max

Hi
I have a HA system on a mobile data bundle which has a cost of $7.50/GB
I bridged the MQTT broker to a broker at a system which has unlimited internet and only share a few topics of interest. Compared to accessing the GUI directly through VPN this reduced data-usage from 200MB/day to 60MB/day but I want to go further
I suspect HA is regularly checking if there are updates. Can I disable this?
I found you can use the CLI to disable the superviser auto update with the command

ha supervisor options --auto-update=false

would this also enable checking for updates of the core and addons?

Are there other things using data I should be aware of?