Happy new year, simmers.
Maybe this is workaround for this issue:
・Before "Move Household", move all the furnitures into the household inventory by your self.
I can confirm that being to use all objects normaly.
But I don't have "For Rent pack", so about new Lot type, I can't confirm.
If someone, having "For Rent pack", try the above way, please post the result. That help for owner of the pack.
EDIT: (May 20 2024 JST)
Caution
In the case move household from Tiny Home Residential Lot and Haunted House Residential Lot, I confirmed when you do the workaround, you have an another issue which the items like collectibles, foods, books and so on put into Storage type objects are disappeared.
The way to workaround is put out items from objects and put into Sim's parsonaly or Household inventory before move household. And then you put all objects in house into Household inventory by your self from Build/Buy mode and move household.
And more things. If you use a strage box which be able to put into inventory like Eco EP's one, you do NOT put the box with items into Sim's parsonaly inventory. Ownership on the box keeps but it possible to lose the items in the box. This case also workaround to put out the items from the box and put into Sim's parsonal or Household inventory. And be careful the number of the items. If the number is over 99, there's a possibility of occuring the other problems. Be careful.
Hope this help.