[robrain]

Settings, Accessibility, Motion, switch off Auto-Play preview videos is supposed to do the trick for System Apps (including messages, safari etc).

Untested since I run my phone via Wireguard to my home network and block everything there.

[lapcat]

This is incorrect. The setting does not apply to Safari. It's for App Store, for example.

[robrain]

Now tested - you’re right

[SenHeng]

I’ve always wondered about this, does it stop downloading the video when it stops playing?

My guess is no.