The question was edited to add that they completed a W-4 at the start of work.
In order to withhold money for Medicare and Social security the company would have had to know your social security number. They would have gotten your social security number from a W-4 or a W-9 form. The W-4 if you were an employee; a W-9 if they were expecting to pay you more than $600 as a non-employee.
Because you filled out a W-4 you were an employee:
We get questions every year about the minimum amount to trigger a 1099.
There is also a minimum amount to trigger a W-2:
Complete and file Form W-2 for each employee for whom any of the
following applies (even if the employee is related to you).
You withheld any income, social security, or Medicare tax from wages regardless of the amount of wages; or
You would have had to withhold income tax if the employee had claimed no more than one withholding allowance (for 2019 or earlier
Forms W-4) or had not claimed exemption from withholding on Form W-4;
You paid $600 or more in wages even if you did not withhold any income, social security, or Medicare tax.
It appears that you fell into group 1. And they should give you a W-2.
So why no federal withholding? The way the tax tables/software works when generating the paycheck, if the gross income was less than $12,400 then you wouldn't have to pay income taxes. To get to $12,400 in a year would require just over $475 in income in a two week check. Your pay for the two days was below that threshold.
If you filled out a w-9 they didn't consider you as a employee. The income you earned was well below the $600 level that requires them to issue a 1099. But they withheld social security and medicare, therefore they thought you were an employee. That doesn't make sense.
I would contact them. They might not have realized the requirement, or it was lost in the mail or misplaced. It is also possible that you agreed to electronic delivery of tax forms, and you will have to go to a website.
I am only addressing the ~$300 in income you had from this company.