The photo and the picture don't seem to match.
To me, a Washington State plumber, it's not right for inspection.
The toilet needs to be vented within six feet. A kitchen sink can't be used to vent it.
A lav can, if you are running 2" for the lav and vent, within six feet. Once other waste is coming down the line, it's no longer a vent. I say that noticing that the lav is on the other side of a 3" main waste line.
If that 3" near the toilet is truly a vent, you could throw a santee off the vertical and trap over with a 90.
If there is plumbing coming down the stack, then that wouldn't work. Without seeing a drawing going through the roof, it's a bit hard knowing what the plan is.