You can use a magnet to poke around down the channel where the missing pushrod used to be. Use a flash light and magnet to see if you can find the pushrod. If left internal, it can damage the other parts such as cam gear, governor, and more. If they are not already damaged.
The pushrod likely bent when the rocker arm ran into the top of the valve guide. Unless the valve seized in the guide and would not move, the only other thing that comes to mind to stop the rocker arm from moving is the top of the valve guide. The guides are pressed into the cylinder head. If the head gets too hot, the guides can migrate upward and finally move enough that they collide with the rocker.
You may(should) remove the blower shroud covering the engine & flywheel. It may be that you have a good accumulation of grass clippings, or even a mouse house that are blocking airflow over the finned area of the engine. Without the cooling airflow, the parts get hot and move around in an uncontrolled manner. Damage ensues.
You can compare valve guide height by measuring the distance from the top of the cylinder head(base of the valve spring) to the top of the guide. As a general rule, they should all be the same. If one is higher than the others, it has moved and is likely the cause of the bent push rod. Replacing with a new push rod will NOT fix the problem if the guide has moved, it will just re-occur almost instantly.
So, remove and clear the cooling, check guide height, and if the guides have moved, repair. There are articles and likely YT videos that explain how to push the guide to its proper location, add some Loctite before doing so and finally use a punch to 'stake\ the guide in place. Many report long term success by doing this.
You will have to remove the head to push the guides back as the valve(s) must be removed prior.
tom