I didn't think Mei was so bad here. She did communicate. She made it clear that Arata is not and should not be considered a rival for her affections whatsoever. She reaffirmed that they're engaged and strongly questioned why Yuzu would even consider anyone a rival still.
If anyone is being the same, it's Yuzu. Mei realizes Yuzu is uncomfortable and says as much, but she also explains to Yuzu that she has no choice but to work with Arata to complete this important project. Yuzu shouldn't be so worried after that, yet she still is even though Mei has never shown a single drop of interest in Arata. If anyone is having to do work for the relationship right now it's Mei not Yuzu.
Then we see that even in private Mei is worrying and thinking of how Yuzu is feeling. If anyone is being unreasonable, again I'd say it's Yuzu. She should have more trust in her partner and should recognize her issues as personal ones she needs to work through. It takes two to party and Mei has made it clear Arata isn't even an option, she only sees Yuzu. So what he feels is irrelevant, exactly what Mei said. This is literally Mei's job and Yuzu is throwing a fit because of a coworker based on gasp Mei having conversations with him! The horror. I hope they don't confront Mei in her office over something she hasn't even done. It's these things that make Mei upset and I can't blame her. Work is stressful enough.