If your stay in Chicago was temporary and you never gave up your New York residency, you would file your 2021 return as a full-year NY resident. To verify you never established IL residency, you can check with the IL department of revenue.
You would also have to file a nonresident Illinois return since you were there more than 30 days. Illinois would have the right to tax the income you earned while you were there, even if only temporarily.
This is the correct way to file and it could set up a sticky situation depending on who your employer is. If your employer was NY-based and you were telecommuting from Chicago, NY considers that to be NY-sourced income in most circumstances. NY is your resident state and considers your income to be NY sourced even while living in Chicago. Illinois considers your income to be Illinois sourced while living in Chicago. Both of them want to tax it.
Generally how it works is your nonresident state taxes the income and your resident state provides a credit for the taxes paid to your nonresident state. However, since NY doesn't consider this income to be sourced in Illinois, they may refuse to offer this credit which would result in being double-taxed.
If your employer was not NY-based, then this should not be an issue.
