Correction: Ch 5 established MC and Shouya are in a "cooling off period". We didn't see any interactions since ch 1 and MC is very complacent about it
With how non-confrontational Japanese is, I (and most of us) missed the context that "taking a break" in a relationship is more like "let's take a break and see other people". At least in the MC's mind. My interpretation of English is the former is still dating while the latter is a soft breakup with a (perhaps insincere) option to reconcile. It can still cause issues but it's a bigger step than it appeared.
Japanese language and norms shifts the line, not even very far, but it makes quite a difference here! The "break to see other people" in English has some very Japanese-like context that's probably close to what the MC meant: it's purposefully vague to spare (or reduce) blame, it leaves space to reconsider, it's easy on egos, socially it saves face, and crucially there is
intentionally space for miscommunication and willful misinterpretation to facilitate the agreed actions non-confrontationally.
And I think it likewise still can cause issues because what it leaves to interpretation, and it can cause drama, surely will cause drama in this series. But with misinterpretation built into the exchange (in both language's variants) no one is in the wrong for treating a quasi-break-up as a real one. However this is a case where seeing another person and it reaching your ex's social circle will likely cost them face, so MC still crossed a line a bit (she's too gay not to).
The new couple in this manga aren't dignified or respectful, sure, that tone is real, but they're not cheating (on purpose).