Don't know what it is but I see in the last shot it is grafted onto a trunk which is falling over. Doubtless the understock is the same terribly rootbound type I see conifers grafted onto here. You may have to do something about that, such as stake it.

The roots are probably too knotted to correct now. If you want a lasting specimen maybe learn how to root conifers from cuttings and start a new one from the scion. On its own roots it might also grow more slowly than grafted onto a seedling of normal vigor.

It looks very much like Chamaecyparis obtusa 'Nana Lutea' to me.

Note also that the rootstock is buried too deeply. The mulch and maybe some of the soil should be pulled back so that the crown is level with the surface of the ground.

I doubt any rootstock on this plant, easily raised from cuttings. I would also go for 'Nana Lutea'

Now it looks like a big piece of mulch lying on the ground next to it. A C. obtusa (or similar species) rootstock would have a different surface to it also, fibrous and darker.

Should I attempt to position the trunk more vertically? I can dig a large area around it and straighten it up.

"I doubt any rootstock on this plant, easily raised from cuttings."

"C. obtusa (or similar species) rootstock would have a different surface to it also, fibrous and darker."

Could be grafted as a small standard at 12 inches or so on Thuja understock which would account for the smooth bark. I know Iseli used to graft on Thuja when creating standards. Not sure if they still do.

"Should I attempt to position the trunk more vertically? I can dig a large area around it and straighten it up."

I would examine the depth at which it is planted and replant if needed, then I'd use a small stake to give it the support it needs to stand straight.