Wood – Strong wood coating

It seems like a new finish of any kind is going to be somewhat at odds with a weathered, distressed look. That said...

A water based urethane finish should change the color less than an oil based one, but there will still be a change. A final coat of satin sheen finish over the initial coats might be simpler than the steel wool and less likely to change the texture of the distressed wood. You may want to use fewer than normal coats of finish, or thin the finish so that it doesn't build up as much as one might normally want on a "new" piece of furniture.

Some sample boards would definitely be the way to go here.

I've used the steel wool + vinegar method before*. It's essentially a stain so really only affects the surface layer. It shouldn't have any meaningful affect on the strength of the piece of wood. Splitting and warping is related to moisture and drying so wouldn't really be affecting by weathering stain.

After you weather it, note that most any additional finishes will change the color. With pine (and actual drift wood) I've found both water and oil based polys will give it a slightly darker, slightly yellow tint (varnish will typically add color as well). So definitely use test pieces before committing.

Rule-of-thumb is that water-based finishes will add less color than oil-based finishes. That said, if the goal is to 'age' the wood, perhaps no finish at all is suitable. Let it age even more in use. :)

PS (*) one trick is to pre-'stain' the wood with black tea. This puts more organic material into the surface of the wood for the oil and vinegar mix to react to.