Does a fixture connected directly to the ground stack (vented) need to be vented separately?

I'm adding a shower in the basement (there was a half-bathroom already) and the new drain is literally right by the stack (probably few feet away, 3-4' max), so I would think the air coming from the stack itself (which is vented in the upper floors) would be more than enough to prevent any siphoning here, but I want to make sure that is the case and find out what code says about it. What are the conditions for a pipe to be acceptable as a wet-vent?

And, if I can't use that as a wet-vent, would an inline vent (like sure-vent) suffice in my case?

Thank you in advance for your insights.

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Edit:

here is an actual image ( the Pex pipes are only there to get the copper pipes out of way! )

I also draw where the new shower drain will go and the possibility of a cheater vent in the wall.