My friend was looking through my collection for foil cards and commented that it would be great if you could search by such soft options as:

Foil
Promotional
Textless
...etc

I looked around but couldn't see anything that would let me do this.

Yep, this is not yet possible, there are no filters for specific card properties like that.

There will be in the future, as it's definitely good to have.

Has there been any progress on making collections searchable by card properties?

Nope, currently still not possible

Thanks for the quick reply. I love the site and will wait patiently for this particular search option to become available.