We of course use our own product every day and when I first joined the company in 2019 I also found that threading felt "bolted on". Primarily because channels rendered everything in the same linear feed regardless if it was a message or comment so there wasn't much point in taking the time to first hit reply.
However, Collapsed Reply Thread [0] has been a game changer for me and not only do I no longer feel that way about threading, my productivity would plunge without it. That feature has been in public beta since last summer [1] and will go into general availability in two weeks to officially become the "right" way to use Mattermost. Not to say that it's the same as Zulip, just sharing an updated perspective.
[0] https://docs.mattermost.com/channels/organize-conversations....
[1] https://mattermost.com/blog/collapsed-reply-threads-beta/
I'd also still like to help you setup tools that your team already use if it's still relevant. Please talk to us in the ~Ask R&D channel on our community instance: https://community.mattermost.com/core/channels/ask-r-and-d
Threading feels bolted on in Mattermost, but is the primary feature of zulip.
Think of Zulip as a realtime version of NNTP, and Mattermost as a more modern IRC with a "reply" feature. The "right" way to use Zulip and Mattermost is quite different, though each one can be easily used as an inferior version of the other.