Use zuliprc files for getting Zulip configuration in integrations

[timabbott]

See https://github.com/zulip/zulip/pull/25826#discussion_r1210613106 for context.

We should probably audit our integrations in this repository for this pattern more generally; it's just a lot simpler as instructions suggest using a zuliprc file, and has advantages for our ability to change things too.