First start of the mower this year and it’s idling wide open. I have never had any trouble with this mower and don’t know anything about it mechanically. Specifically, I can’t figure out how to adjust the governor as there doesn’t seem to be any way to. It’s different from my Briggs riding mower and every other push mower I’ve seen. Searching the internet yielded nothing and led me here. Any help is appreciated.

I was going to upload a couple of pics, but they wouldn’t load.

Is throttle plate closing? On the pictures are you doing it in mobile or full version?

I took the pics with my phone and tried to upload them. It would get to 61% and no more, so I gave up.

I didn’t check if the plate would close. Tomorrow I’ll manually close it at the carb and see what it does.

I worked the governor arm by hand and the rpms went down, so I assume the throttle plate is closing.

There should be a small spring (not showing on the parts diagram) that attaches to the exterior governor rod and to a static piece of metal...  The top RPM is adjusted by bending the arm causing different tension with the spring.
 
Below is a pic of a customers machine I currently have apart.  Make sure you have this spring and it is attached as shown (likely your issue):
 
 
 
 
If it is there it's possible your internal governor has failed, part # 43:
https://www.ereplacementparts.com/briggs-and-stratton-09p7020027f1-engine-parts-c-16758_17347_233724_233751.html 
 
Check and reset the governor if need be.  
 
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There should be a small spring (not showing on the parts diagram) that attaches to the exterior governor rod and to a static piece of metal...  The top RPM is adjusted by bending the arm causing different tension with the spring.  If that spring is broke/missing, the RPMs WILL be extremely excessive..
  

The spring is present and seems to be in good shape. I’m out of town this week, but I’ll try bending the arm when I get back. I guess if that doesn’t fix it, then next step is taking the engine apart to check the governor?

Brx76
The spring is present and seems to be in good shape. I’m out of town this week, but I’ll try bending the arm when I get back. I guess if that doesn’t fix it, then next step is taking the engine apart to check the governor?

If the spring is still there, with the "wild running" ,  it's not the issue
 
I'd check the governor adjustment first, then the side cover removal to access the mechanism itself.
 
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Mine looks like the picture you posted above, but I don’t know how to adjust it. I’ve adjusted the governor on my riding mower but it’s a different set up. On my push mower, the fly wheel and electric shut off seem to be in the way. Or I don’t understand how this one adjusts.