Another possibility is to not include content in the push messages and just send an "there is new content" using the official Zulip push service.
If you run a Zulip server, you can have it send mobile notifications without needing to compile the mobile apps yourself. Lots of people do that, though their motivations may be different from the grandparent's.
This does mean sending the notifications through a central notification "bouncer" service which we run, and that page of our docs explains why the way Google and Apple have designed their push-notification systems makes this necessary.
We're working on end-to-end encryption of the push notifications: https://github.com/zulip/zulip/issues/6954 Once that's done, that will mean that the content can't be read by the bouncer service, nor by Google or Apple en route.
(OT: The one thing I still miss on Android is the handling of the share Intent)
Here's the issue: https://github.com/zulip/zulip-mobile/issues/117
Here's a recent (~3 weeks old) and active pull request: https://github.com/zulip/zulip-mobile/pull/4124