Is the 05 Legacy remote the same one Subaru uses for the Baja? I know some companies use a remote with a trunk symbol of a car, or an SUV/Truck symbol for the SUV/Truck types...

From my experience, the remote should be the same.

So I can program this remote to an 05 Baja just like a legacy? https://www.thepartsyouneed.com/displayProductDocument.hg?productId=1775

I should have been clearer, the remote for the pre-04 Legacy was the same, that one won't work on the Baja.
Try this one:
https://www.thepartsyouneed.com/displayProductDocument.hg?productId=1771&categoryId=34
Or better yet, they sell the same remote and just label it as a Baja remote.