So you've got basically two options to vent the WC.
Option one is to install a dry vent takeoff near the WC with a new dry vent in that left hand wall. The challenge with that is that the dry vent is supposed to rise vertically until 6" above the flood rim of the WC. "Vertically" here means up to 45 degrees off plumb. Since you're meeting up with a drain whose center line is 15" below top of slab 8' away, the WC fixture drain will need to be no more than 13" down when it turns horizontal.
You could take a vent off as the WC drain turns from vertical to horizontal by using the following sequence: closet flange, vertical pipe, the branch inlet of a wye, then a street 45 for the drain to turn horizontal. The straight inlet on the wye is your vent (with a 3x2 reducer or bushing as you only need a 2" vent) and is at 45 degrees off plumb. But I think it doesn't end up low enough, given that the closet flange is 12" off the wall, I think the vent would emerge from the slab before it makes it into the wall.
An alternative way to take a dry vent off the WC drain would be to route the horizontal portion in plan towards one of the two side walls, so then a dry vent could rise up out of the slab under one of those walls. There's also an allowance in the UPC for the dry vent to turn horizontal below the slab when structural conditions preclude its rising vertically. But with the allowance for wet venting now in the UPC, I'm never clear when that horizontal vent allowance applies.
Option two is to wet vent the WC from the lav, which is the typical solution. The WC drain goes to the right as normal. The lav drain is 2" (with a 2" vent) and you reroute the lav drain to go down into the slab and then down the page, joining the WC drain with a horizontal wye or combo. That joint is the vent for the WC, so it has to be within 6' of pipe length from the closet flange.
Either way, the shower gets vented separately; if the existing stack on the right is a vent stack only with no drainage from a story above (lav drainage is OK under option 1), then the shower trap and trap arm can be at a higher elevation than the WC drain, joining the stack with a san-tee, which vents the trap arm.
Cheers, Wayne