It really is a graphical redundancy. I didn't find any data about it, but here I describe my perception in case of justifying its use
I start from the basic meaning of the arrow symbol = next, ahead, go ahead. If a CTA implies the fact of jump, advance or change, the use of the arrow on a text button could be allowed in the following cases, all of them to differentiate them from other CTA buttons:
To differentiate actions that will be carried out on the same page or outside:
The image shows that the only arrow in principle redundant is the horizontal one from left to right
→ since the text itself indicates a change or jump. The other arrows implies actions that will be carried out on the same page
- Beyond the direction of advance shown by the arrow, it's also a
visual way of indicating the form is not yet complete, for
contrast, the user will know / see that they have not reached the end yet.
- In the case of forms, the arrow makes more sense when there's the possibility of going back to the previous step:
When the text doesn't make any direct reference to the action, although it does imply a next step:
In menu items the arrow has a double meaning: the uncollapse action to show the hidden content.
In a text/icon CTA buttons group when the arrow icon corresponds to its real definition