she likes carrying around random rags for no reason

This is actually a common trait of golden retrievers! They’ll do it with toys, socks, rags, etc. Holding things in their mouths acts kind of like a pacifier to them and is much like a coping mechanism to help them handle their emotions (both good and bad). Our golden usually grabs our socks and carries them around when happy to see us, or when she gets scared or embarrassed.

my saint bernard carries our bras over to her spot when she misses us

I had a friend once who owned two golden retrievers and whenever you’d visit her house, one of them would become so happy, he would immediately walk up to you, gently “grab” your wrist with his mouth and lead you around the apartment. Totes cute.