Shift swaps without the group chat

A swap in a group chat needs three things to go right: someone offers, someone takes, and the manager notices. The third one is where it usually fails (sample guide).
Set one rule: a swap only counts when it shows on the rota. In the staff app the person offering the shift posts it, a colleague takes it, and the manager approves with one tap. The rota updates for everyone.
Keep approval on for the first month, then switch it off for swaps between people with the same skills if you trust the team.