Nothing wrong with a shim, I too like a low action and have put plenty in but I try and make sure they fit across the pocket and taper toward the open end of the pocket.
I’ve used veneer and card (mulched wood) and some fine emery cloth to achieve this.
There is an argument that shims can expedite a ski jump at the end of the neck but there are also those that argue against if done properly.
All major (and a few minor) manufacturers have used shims from the factory.
I’m not too keen on the shim you have there but I’ve seen it done a lot as a quick fix, I would be replacing it with a decent shim and not worry about it
As for the refret, the neck (and bass?) is 59 years old, if it’s been played and loved since day one it probably needed it.