I think you need to separate punishment from basic belongings.
If she’s 13, she’s still a child, and whatever’s gone on recently, she’s entitled to her personal things like clothes, toiletries, school stuff, her phone/charger, books, sentimental bits. That isn’t “rewarding bad behaviour”, it’s just making sure she’s not stuck at her dad’s without essentials.
But anything that’s part of your home like furniture, bedding, décor, bigger items you bought to stay in her room, those stay put. If she’s choosing to live at her dad’s for now, then he needs to provide the actual setup there.
I also wouldn’t get into a power struggle over collecting the items. Let her take what she needs, keep the tone neutral, and don’t rise to whatever narrative her dad is spinning. Kids who run off to the other parent because they don’t like consequences almost always circle back once the dust settles. Because once Dad has to cope with the reality and his patience wears thin, he will stop being the daughter pleaser she knows (anyone can keep it up for a couple of days but not permanently) and try actual parenting, then she may reconsider the move.
Give her the basics, keep the boundaries, and don’t make this the hill you die on. The relationship matters more than the possessions.