I reckon the problem you are having with Autofill is that the initial cells you are entering manually are being recognized as text rather than dates by Numbers.
To see if my estimate is correct, I suggest you select the first date you have entered manually and check what Numbers show at the bottom left of the screen. I expect, in your case, it says "Text Fri 1 Apr" for the corresponding cell. This means Numbers is recognizing the "Fri 1 Apr" you have entered as text rather than a date as also shown below.
To resolve this, the initial dates you are entering manually should be in a form that Numbers can automatically recognize as dates. For example, enter "1 Apr 2022" manually as the first date. Then Numbers would automatically recognize this as a date rather than text and show "Actual 01.04.2022 00:00:00" at the bottom left (or "Actual 04.01.2022 00:00:00" if your macOS region settings are for US/UK). Next, you can enter "2 Apr 2022" into the next cell and then use the autofill to fill the rest of the cells as needed.
You may note at this point, while the autofill might be working correctly with this procedure, the dates in your own table are not formatted as you originally intended in your question and also unlike those in the table I gave as an example above. To get that date format, you need to use the "Custom Format" option available through the sidebar menu in Format > Cell > Data Format as shown in the picture below. You can learn more about custom date formats in Numbers under the "Create a custom date and time format" section in the "Create a custom cell format in Numbers on Mac" Apple Numbers support webpage if you like.
The autofill should take care of the formatting for the rest of the dates it creates, but, in case you need to copy the custom format you have created onto other cells, you can use Format -> Copy Style and Format -> Paste Style commands available in the Numbers menu at the top.
In case you work with dates & durations frequently while using Numbers, I suggest you watch the nine-minute video titled "Calculations With Time and Duration Values In Numbers" by macmost.com.