What you do for overload protection depends to a certain extent on how you use the converter. If it's only ever going to be used with the one machine, and especially if it were hardwired, then the overload protection on the supply will also cover the machine if it is sized correctly.
But if the converter might be used with different machines, then you'll need overload protection for the converter, and separately for the machines.
From the description, there may already be some protection installed. Motor starters are usually (but not always) fitted with overloads - if so fitted then that covers the motor controlled by it. Since the smaller items (eg light transformer) wouldn't normally be adequately protected by any supply fusing, there may well be a built in fuse in the device itself.
And while considering things like the worklight, it may be worth checking which is the synthesised 3rd phase on the converter output - and ensure that the worklight is wired across the other two. The synthesised 3rd phase is likely to be a lot less stable than the 2 that are created by transformer from the 1P input - so best not to link your light to it.
And if there is a 1P socket for anything, then (and again, you need to know about the internals of the converter) it may be best to remove it and and use a different socket direct from the workshop supply. As I mentioned earlier, we have a convertor in a box that looks very similar to that at home, it has no neutral, and the 3 phases really don't relate to the 3 phases you'd get ina real 3P supply. IIRC the input L-N is stepped up to 415V with an auto-transformer to give 2 phases - one of which is more than 240V to neutral, and the other is a lower voltage but "negative" relative to the input. The 3rd phase is generated by capacitors and varies considerably with the connected load and the unit setting. Yes, of course I've had the lid off to look inside
A genuine rotary converter could provide a neutral point - but for reasons of economy (it would add to the cost and weight of the machine) it's not likely to and/or it may not be as "earthy" as people are used to with neutrals - ie you'd want to treat it as live and not use any single pole switching downstream.
You may have noticed a certain amount of "if"s and "but"s - that's because to really answer the question means knowing details of both the converter (ie what it's got inside and how it's wired) and the machine (ie how it's wired). There are so many ways these things
can be done that it's hard to generalise.