Icons Registry: Trim public icons further

[mcsf]

Follow-up of #75526

Of the two Copy icons, currently only copy-small is exposed, not copy. Is that still how you'd like it?

I'd like to actually remove both, for now. Here's an updated list that's even more conservative, based on the conversation here.

All that sounds very cautious, I know, but I'm sharing it with excitement. There's fresh energy on icons, and I personally think this means all those icon changes we've been wanting to do for a while gets new priority.

Originally posted by @jasmussen in #75526 (comment)