I had the same problem on a Sears 3.5hp of about the same year. I’ve also had this same problem with other Tecumseh equipment.
Your carb looks like mine, and don’t know if it’s set up the same way, but it’s worth a look.

The inlet needle seat on mine is rubber, and the needle would stick tight blocking fuel. It’s a little bit of a pain to remove. I made a little hook to push through the hole and pull it out. They do make a special tool to remove and insert it. The seat goes in one way, I believe the flat side faces the needle, but don’t quite remember….
I can’t make out the part on the diagram .

Also, replace the diaphragm ( looks like a little rubber hot dog) and clean the passages around it. Pop out the screen and clean there too. Inspect or replace the check valve "flaps" too.

You may be able to get a complete kit on ebay by searching the Tecumseh engine number, or the outboard’s model number.

Here’s some seats on ebay, showing what they look like :
https://www.ebay.com/itm/10Pcs-Replacem … Swy~BaCHCt

And the special tool :
https://www.ebay.com/itm/OEM-Tecumseh-6 … SwGzhaJseh

I hope this helps.
Again, not sure if your carb is the same, so disregard if it isn’t.