I think the purpose of applying soap to the fabric side of a strop is just to fill in the weave, and give asmooth surface.
I have a cotton strop with Dovo white paste (slightly abrasive) but I don't use it much, I prefer plain linen.
On the leather side all you need is something lke Dovo yellow, which is just wax, to keep the leather soft.
Eventually, when the blade starts to lose it's edge you can decide wether to restore sharpness by honing, by using abrasive paste on a dedicated leather strop, or send it away for someone else to fix.