Italy and Dalmatia alone aren't going to have enough resources to live on their own : eventually you'd have a puppetised WRE by its eastern counterpart, if not gradually swallowed up.
Keeping Africa as part of the WRE is really the vital minimum for his survival, in order to have a rich province untouched by most troubles and able to supply with grain and fiscal income (a bit like Syria and Egypt did for ERE).
A still existing WRE doesn't mean it wouldn't harbor Barbarians, especially military speaking, so you'd certainly have to look something close to Orestus, Odoacer or even Theodoric's Italy to have an idea on what it would look like.
Basically a greater actor in most of its former provinces, especially Gaul and Spain, with certainly an interventionist mood (more true for the former).
As such, we could see the Gothic hegemony in Gaul and Spain being butterflied away and Romans keeping Narbonensis, Tarraconensis, Provence and Auvergne (while possibly giving up the latter as they did historically, for a more convenient stuff).
It's possible that more isolated Roman holdings (Northern Gaul, part of Spain) would, without being conquered by Barbarians (at least in a first time) would be more treated as part of a sphere of influence rather than part of the WRE.
That's said, I could still see it being politically troubled by political interventionism of his stronger counterpart, trying to "benevolently advise" it.
For long term consequences, it's really hard to say. I would see Romano-Barbarian kingdoms being still considered part of Romania, but living on their own sometimes allies, opponent or indifferent about Ravenna.
Sort of sub-kingdoms not unlike they existed within Romano-Barbarian kingdoms themselves IOTL : large autonomy if not independence de facto, tendency to have their own policies and expansions.