The TG has a 1/2.5 sensor and no manaul control. I do not dislike the TG series but it is a pretty much minimal camera in capability, dynamic range, IQ but compared to a phone in a case it can drive strobes.
The Backscatter strobe does have a built in video light whereas the Inon does not. I think it does anyways.
Since the OP once owned a Nikonos, and if money was not a huge constraint, I would and have been tempted greatly to get the Cann G7 in a Nauticam housing. The G series canon and the Sony RX series have one inch sensors which are comparatively huge and fully capable of producing great photography and huge blow ups ands have excellent dynamic range. And they have full manual control and actual F stops instead of a ND filter to simulate a f stop as does the fully automatic only TG.
As
@Barmaglot suggests, a single strobe center mounted on the cold shoe could work for some shots and video with limited expectations. I mean, folks do not put strobes on arms just because it is fun, it is done for a myriad of reasons.
I have put my Canon S90/FIX rig back into rotation with my Sony Nauticam because it actually can do somethings more easily (not more better

) than my NA6400 and it is smaller when folded up and lighter. Not shown in the pics below, see that center ball in the cold shoe, yes, I can and do run a single strobe there and remove the double arms and in such case the FIXS90 is a tiny, little bitty thing, smaller than a Nikonos: