I am working on a remodel of a shower that was originally wet vented. Currently the shower ties into the main 4" sewer line downstream of a toilet, so I would like to add a dedicated dry vent to help prevent any siphoning of the shower p trap from occurring.
Have you had any problems with siphoning? Wet venting works when implemented properly, so you may just be making more work for yourself. Having the shower wet vented downstream of the WC would require that you are under the IPC, not the UPC, and that the branch drain the shower connects to is carrying only bathroom fixtures from at most 2 bathrooms. [Although I guess there is a little more flexibility with so-called circuit venting, which I am less familiar with.]
As to your venting question, that's a slightly tricky question.
Technically the answer is no, as the IPC and UPC both define "vertical" as at most 45 degrees off plumb, and require the dry vent to rise vertically until at least 6" above the fixture flood rim.
However, a common way to take a dry vent off a horizontal trap arm that stays horizontal is to use a wye that is rolled 45 degrees off being upright-most. That similarly produces a vent with an elevation angle of 30 degrees, meaning it requires a 60 degree elbow to turn vertical when the vent gets under a wall. That this practice technically violates the "vertical" requirement seems to be almost universally overlooked.
Whether your jurisdiction would take the same attitude towards the configuration shown I can not say. One difference from the previous case is that your vent starts off vertical and then reduces its elevation angle, while in the previous case the vent takeoff starts off at a reduced elevation angle.
Can you shift the san-tee over far enough that you can use 45s for your vent and stay within the wall, and then offset the drain location below the san-tee as required?
Cheers, Wayne
P.S. A sewer is a sanitary drain (sufficiently far) outside the footprint of a building. You presumably wanted the term "building drain", which is what exits the building to connect to the sewer.