I have announcements turned on but they are not announcing that I picked up the item.

It's bad copy.

"I'm in a group."

"What kind of group? A party, or a raid?"

It uses "group" when it means "party" and it has some "both" option.

Options should be:

None
Group
Party
Raid

Party by Default is fine.

So there is nothing broken, but the "Group" setting is not clear enough to mean "Party", do I understand you correct @Gogo1951 ?

You aren't using default wow language.

"Group" is a party or a raid. It's what you are calling "Both" but you're using it as "Party."

You're making up your own language here, when perfectly suitable language exists.

It's bad UX.

I count that as a "Yes".