I have built some of the items requested by Poe for his safe space quest in my home Abeyance / Respite. Each time I return to Respite it increases the counter on the number of items I have built - e.g. I have one single bed but after returning to respite numerous times it has gone up to 24/1. This appears both in the tracking and in the Journal area.
I thought you had to build those items where Poe is located? Does it count if you build them in your own realm? That would certainly make it a lot easier and cheaper.