test_message_fetch: Reorganize web-public tests.
test_message_fetch: Reorganize web-public tests.

With some extensions by tabbott to cover adjacent corner cases.

Fixes #20288

zulip/zulip,andersk/zulip,kou/zulip,rht/zulip,zulip/zulip,rht/zulip,kou/zulip,rht/zulip,andersk/zulip,rht/zulip,rht/zulip,zulip/zulip,andersk/zulip,andersk/zulip,andersk/zulip,kou/zulip,zulip/zulip,kou/zulip,andersk/zulip,rht/zulip,andersk/zulip,kou/zulip,kou/zulip,zulip/zulip,kou/zulip,rht/zulip,zulip/zulip,zulip/zulip