module.exports not accepted as proper JSDoc for autocomplete

I have three files to demonstrate this issue:

class.js:

/**
 * @class Main
 */
class Main {
  /**
   * @param paramA
   * @returns {Promise<number>}
   */
  async someFunction(paramA) {
    return 1
  }
}

testdoc.js

/**
 * @typedef {Object} TestDoc
 * @property {TestDoc.TestDocCallback} func
 */
/**
 * @callback TestDoc.TestDocCallback
 * @param {Main} y
 * @returns {Promise<void>}
 */

test.js

/**
 * @type {TestDoc}
 */
exports = {
  func:async (y) => {

  }
}

Given these, when I type "y." in the editor, I should get an autocomplete menu that relates to the class Main. Instead, I get the default autocomplete: constructor, etc.

But, if I change test.js to this:

/**
 * @type {TestDoc}
 */
let exports = {
  func:async (y) => {

  }
}

Autocomplete works fine. "y." pulls up the function with the return type and everything. So just by making it a local variable rather than a global, it starts to work. This is the case for any global vs any local variable name I could think of. What is going on?