My suspicion is that someone had chemically stripped it & the roughness you feel is the wood "whiskering"
if it has been sanded it will be apparent if you wipe a little mineral spirits on it and look for scratch patterns. If it was chemically stripped they prolly used a green pad or steel wool... look for green fibres. use a straight edge on parts that are supposed to be straight & look for peaks & valleys, if a sanding block was not used, they will be there.
the only reason to sand this thing would be to address a defect or prep for finish, if it is whiskering light 0000 steel wool in the direction of the grain to remove the whiskers, not material, just the whiskers. it looks very good I do not see any reason to sand it.
Don't oil, there's enough glue in there that it's basically a piece of plastic right now anyway & you won't get great penetration
Your finish should be dictated by its end use.
Varnish can be tinted, levels well and will be easily reversible, get whatever coloring you want out of it and will be pretty durable. Varnish (at a guess) will probably be more 'historically accurate' than an oil finish anyway.
