Toilet shutoff valve is leaking at the stem

The toilet supply line is leaking around the shutoff valve stem, not at the tank connection. It’s a slow drip, but the valve also won’t turn fully closed.

I’m trying to decide whether to replace the shutoff now or contain the leak until a plumber can get here. If the valve can’t isolate the toilet, I assume the main water supply may need to be shut off before disconnecting anything.

Would a temporary clamp or cap actually be appropriate for this type of leak, or could it make the valve or supply line fail suddenly? I’m also wondering whether gently tightening the packing nut is reasonable, or risky when the valve is already stiff.