Is it possible to get the acting party in the init and update functions of a Trigger?

The rule takes the acting party as an argument, but the initialisation and update functions don’t. How do I find out who a trigger acts as in those functions?

Right now you can’t do that. You can for read as parties via getReadAs and there is no reason why we can’t expose something similar for act as. I’ve opened Expose acting party in trigger outside of rule · Issue #12125 · digital-asset/daml · GitHub to track this.

Starting from next week’s snapshot you can use getActAs to get access to the party in init, update and the rule.