First off, "autotransformer type Wye/Delta starting" are mutually exclusive terms; it is one or the other, not both.
So that said, that's definitely not part of an autotransformer starter and I think Gunnar is right, it looks more like it is part of a controller for a Wound Rotor Induction Motor (WRIM), which would have slip rings connecting the resistors to the rotor of the motor (that's why he asked). The devices in that cabinet look like resistors that are used to control torque and speed. If it is a WRIM, you CAN retrofit them with a VFD if you need the speed control, but Gunnar's points on the motor not being made for that are valid, so you would need to take extreme measures to protect it. it can be done however, I have done it numerous times successfully. It just is not something you do on the cheap.
It is also possible to use a soft starter on a WRIM if you do NOT need to change the speed, but there are steps you must take to engineer the soft starter into the system, usually involving testing how the controller works NOW with your load. But for you that means hooking up that controller now just to find out, only to rip and replace it later. Kind of a lot of effort.
The other remote possibility is that they used what is called a "Closed Transition Wye-Delta" starting scheme, and those resistors are being used in the transition stage (it's complicated to explain to someone who doesn't know what it is, so just go with it for the time being). But typically you would not need that many resistors. I only mention is because it appears as though MAYBE only a few of them are wired to anything, it's difficult to tell in that photo. That may indicate that someone recognized what a nice resistor package that is and re-purposed it for use with a closed transition W-D starter. The good news if that is the case however is that it becomes a VERY good candidate for replacing all that with a solid state soft starter.
Can you take a picture of the motor nameplate and/or the starter itself?
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington