Combine first 8 ingredients (through bay leaf) in a 6-quart Instant Pot®. Close and lock the lid of the Instant Pot®. Turn the steam release handle to "Sealing" position. Press [Manual]; select "High Pressure," and use [-] or [+] to choose 23 minutes pressure cooking time. When time is up, open the cooker using Quick Pressure Release (page 4). Remove chicken from broth mixture; cool slightly. Remove chicken from bones; cut chicken into bite-sized pieces. Discard bones.
Strain stock through a sieve over a bowl; discard solids. Return inner pot to cooker; return stock to inner pot. Stir in chicken, hominy, chile powder, and oregano. Let stand 5 minutes. Skim fat from surface of broth; discard.
Ladle stew into 8 bowls; top each serving evenly with pumpkin-seed kernels, cilantro, radishes, scallions, and queso fresco cheese.
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