Chat groups win because they are fast. Any replacement that is slower will be ignored, whatever the policy says — so the goal is not to remove the phone, it is to make the phone produce a record.
Keep it to one screen and one tap
A manager walking the property will approve from a notification. They will not open a laptop. If approving takes longer than sending a message, the chat group survives.
Record what the decision was based on
The valuable part is not the approval, it is the evidence beside it — the punches the overtime was checked against, the balance the leave came out of. That is what answers the question six months later.