Instead of holding R and then left-clicking a tool to select, it would be quite nice if there was an option that allowed a player to select a tool by simply holding R, moving the mouse in the loose general direction of the tool, and then letting go of R.

Quite like the system in Half-Life: Alyx if you've ever played that.

That option exists. go to your toolbelt-client.toml file and set ReleaseToSwap=true. You can also enable the option to allow selecting out of bounds, or the option to contain the mouse cursor within bounds.