Yes, but you can’t do it with that date field, because unfortunately Airtable doesn’t give enough variety of formatting options for date fields.
So you’d have to create an additional formula field that formats the date field the way you want it to look using the DATETIME_FORMAT function, and then you can group on that new formula field instead.
However, the big problem with this is that Airtable will try to group your new formula field alphabetically instead of in date order, so it becomes a challenge to keep your records in the right order. So you will need to format your date formula in a completely different way to keep the dates in order, such as “2021-12-25 Sat”.
Alternatively, you can keep the grouping in the exact same way that you have it now, but just add another formula field that shows you the day name for each record. So the day wouldn’t show on the grouping bar, but it would show on each record beneath the group.
Airtable is a real pain when it comes to all of this, and I would recommend emailing firstname.lastname@example.org to request that they give us more date formatting options on actual date fields.
In my main planning base, I only use about five or six fields consistently. I just took a look at how many were hidden in the view that I use the most: 43. It may seem like a lot, but each one has a specific function in the design of the system, including custom group labels in a few cases. Could I get by with fewer hidden fields? Sure, but even if the purpose of a field is just to provide a specific group label, that cosmetic contribution adds meaningful value to the system for me, so I’m fine with 43 hidden things that each add value in some small way.