This is how the Government calculates the entitlement.
https://bit.ly/3G25m6g
An employee gets 1/12 annual entitlement for each month or part of month worked and that is rounded up to the nearest half-day or whole day.
In your case, you will have been employed in four months or one third of the year. That means your entitlement is
4/12 × 28 = 9.3 rounded up to 9.5 days.
When I worked for DWP, we had calculators for full-year, part year, change from full-time to part-time, change from part-time to full-time, you name it, we had a calculator.
Each one was based on days worked or remaining in a leave year.