[web] Only fetch one page at a time in ChatMessageList

Summary: While investigating another issue I noticed that under certain conditions we could end up fetching a second time before the first fetch concluded.

Test Plan: Make sure we can't fetch again before the first fetch concludes

Reviewers: atul, palys-swm

Reviewed By: atul

Subscribers: KatPo, zrebcu411, Adrian, subnub

Differential Revision: https://phabricator.ashoat.com/D894