Helping an opponent up isn’t a break from competing. It’s part of it.

Competition is a shared arrangement rather than a fight. You both agreed to turn up, follow the same rules and try to beat each other inside them, and that agreement is the only reason the result means anything. Looking after the person on the other side of it is part of the activity, not an interruption. The hand up is maintenance on the thing that makes competing possible.

Put the hand out while you are still annoyed, because that is the version that counts. Carry on playing exactly as hard a second later. If a teammate reads that as weakness, they have misunderstood what you are both doing out there.