When you worked during the year doesn't matter. As long as you have earned income you can contribute anytime. If you are an employee you will get a W2 by Jan 31 to report your income. The W4 is the form you gave your employer to tell him how much withholding to take out for you. It does not get sent to the IRS. The IRS gets a copy of the W2.
if you have self employment income it also counts as earned income. You might get a 1099NEC for self employment.
See IRS Pub 590-A IRA Contributions
https://www.irs.gov/pub/irs-pdf/p590a.pdf
