In theory I suppose it should be possible to certificate the A319 for autoland on a 37m runway.but I imagine the approval process could be long and expensive. The sort of issue that might need to be considered could be unintended autopilot disconnect during rollout in crosswind conditions. Perhaps if such approval were ever to be obtained the Cat 3 limits would be higher than for a standard width runway.
The turboprops generally can operate to Cat 2 with manual landing so it might be argued the width of the runway is irrelevant to them. Cat 2 would enable landings in (say) 350-400m RVR. UK fogs usually seem to stabilise at a figure lower than that, but it would still be much better for the turboprops than Cat 1.
There may be other issues additional to the runway width why Cat 2/3 at SEN may not be practicable. For example, approach lighting would need to be upgraded. Supplementary approach lighting and touchdown zone lighting would need to be installed. The regulations appear to state that nowadays in the UK the Cat 2 and 3 lighting requirements are the same. Would site limitations permit this at SEN ?
Stobarts have not been exactly shy of investing in quality equipment so I imagine they must have examined this issue. The runway extension work would have offered the obvious opportunity to install TDZ lighting as a provision for the future. I would guess they concluded that Cat 2/3 was not economically viable or simply not practicable.
Incidentally on the subject of running costs I am given to understand it is the power requirements of operating the Cat 2/3 lighting that is the major incremental expense.