The gith are looking for it. Considering how important the thing seems to be to them there should be more than one Gith team in the area. Gith are not very good at social interaction with the people in Faerun but they could bribe some locals to spy for them. The mindflayers knew about it, otherwise why shield Shadowheart. If they were in alliance with the absolute, the absolute should know about it and should know from the tadpole that Shadowheart has it. But the absolute and its followers do not seem to care about it.
The Githyanki might be looking for it, but they clearly have no idea who has it and barely know what it looks like.
It's possible Shadowheart was shielded for other reasons, like her flaring magical powers.
The Absolute seems to have been made aware there was a "weapon" inside the ship at some point. It doesn't mean it knows what it is and who has it. Edowin was going to the ship to find a "weapon" but gives no description. His "siblings" believed they were going to rescue survivors. The Goblins/Minthara doesn't seems to know anything.
Shadowheart has self-banter at the Grove (if you don't recruit her at the beach), where she says she just has to keep it safe (until she bring it to Baldur's Gate). That's probably the extend of her knowledge on the matter...
