Is Midwestern the possessive noun for Midwest?

No, the Word 'midwestern' is the adjective form of the noun 'midwest.

Directional nouns form adjectives using -ern. The capitalized versions are the same.

A possessive noun is a form of noun used to indicate ownership, possession, origin, or purpose of that noun.

The possessive form of the noun midwest is midwest's.

The apostrophe s ('s) at the end of the noun indicates possession.

Example:

The midwestern states are known for farm products. (adjective-describes the noun states)

The midwest's farm products are sold all over the world. (possessive noun-the farm products of the midwest)