Ronseal fence stains/paints are renowned for washing off. The water doesn't bead so I don't think they have wax in, certainly not like the Cuprinol Ducksback (which is only for rough sawn) or Garden Shades. Both of which stick properly if used appropriately, IME.
Garden paints generally are waterbased with wax - you know when there's wax in as subsequent coats need applying within a certain amount of time, otherwise they roll off. For Garden Shades & Johnstone's Garden Colours, it's 8 hours (imprinted on my memory as I decided I hated the colour that evening & had to take an emergency trip into town to buy another can).
GS is quite thin, the Rustins variant is too, so you do see the wood grain through - I wouldn't say it's plasticky.
I've not used any of them on furniture yet though, just rough-sawn and smooth timber. I was really impressed with the Rustins coverage on a door.
I'll take a pic later if you want, once it stops ****ing down here.
The Osmo system is oil-based, so totally different.
Have you spoken to a supplier, e.g. Wood Finishes Direct? They're pretty helpful and have been through the different options with me before now. They'll also be aware of supply problems.