Harbor Freight said they don’t sell a 10 hp tapered shaft engine though their generators have them.
I had an HM100 Tecumseh can I install a larger engine?
Tecumseh is no longer in business.

Can I mount it to a piece of metal and make it belt driven? If I can’t find a oem tecumseh engine

You really can't do the belt operated set up.
 
The engine side would work fine however the middle stator is attached TO THE CRANKSHAFT
(centering it and securing it dead center).  With no crankshaft, there's nothing to hold it.
 
I'd keep my eye on Craigslist, etc for a used engine.   The 10 HP Briggs is a very common (and good) engine.
 
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https://youtu.be/XmasTRFYros?si=Ffg858KIZQspQcgM
Like this

I don’t know the model number for the Briggs counter part with tapered shaft. I tried posting screenshot of YouTube video and link where someone made it belt driven.

If the generating powerhead (newer style) is bolted to the side of the engine, the side of the engine 
is PART OF THE GENERATOR.  Technically, one end of the generating power head..
 
Now if the power head is completely separate and a stand alone unit, yes that YT video / style would work..
 
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Id rather it be oem style but if I can’t find the engine or parts bc Tecumseh is out of business I could probably cut off crankshaft and mount or weld a pulley and it would be like the YouTube.
As I suspected my piston connecting rod and cap are in pieces

Pics are not uploading

You can definitely install a larger engine, but you’ll need to make sure it fits the space and aligns with the tapered shaft setup. Since Tecumseh is out of business, you might need to modify the mounting or find an adapter for the shaft. Just make sure the new engine's power output matches your generator's needs to avoid any issues.

If you can get parts number do a search on eBay with part number you may get lucky with a used one