I know of no ‘COTS’ multi turn potentiometer in that small form factor. In my experience such would normally be a custom part, likely based upon a miniature multi turn trimpot topology.
In situations where a miniature multi turn potentiometer is required, I have seen multi turn trim pots used. A small brass shaft is attached to the brass trimpot adjuster. This is not something I would wish to do as it seems like a “hack” but I have seen it used on commercial equipment to good effect. I have no idea of the trimpot life expectancy if regularly adjusted.
There is a temperature calibrator that I own that uses this “adapted trimpot” approach and it has been reliable. Picture attached.
I think the trimpots used in this ‘hack’ are the version with a finger grip adjuster. Picture attached.
Fraser