Does the 3" stack have (seems very likely given what it serves) any toilets entering it above?
If so, it stops being a vent stack (and becomes a soil stack) below the highest toilet entry, and a separate vent stack is needed to bypass around them, under current codes. As far as I can tell that was not a consideration when the cast iron plumbing in the house I grew up in was installed, but things do change with regards to what's considered acceptable.
Or the AAV option for venting. Looks like you are at least planning to put that high, which will improve the odds for it working over time with minimal failures and replacements required.
Under the likely applicable codes for a 2015 build there should be a separate vent for the first floor powder room sink (and toilet, usually via the sink), due to the second floor bathroom above, which you might be able to tie in to, if it's big enough.