per code a pipe is not permitted to touch any concrete in the wall. When running a pipe through a masonry wall we are required to sleeve the pipe. Properly to sleeve the pipe they are required to install a short length of pipe at least two nominal pipe sizes larger than the desired pipe and extending out about 2 to 3" on either side of the wall. The sleeve is then sealed to the concrete wall in any desired manner including casting it into the wall as the pour the concrete if so desired. In some jurisdictions they will allow the foundation contractor to simple place a cylindrical form and pour the wall with the desired hole through it, or they may drill the desired hole through the finished wall when the concrete is set. Later when the plumbers set their pipes through the sleeves they are supposed to fill the space between the exterior of the desired pipe and the interior wall of sleeve with expanding foam. From your description it sounds as if they didn't inject the foam in the hole. The simple solution would be to use a water hose to wash as much of the dirt, sand and silt out as you can then fill the hole with expanding foam. When it hardens the hole will be sealed.

Adding any sort of waterproofing to the inside traps the water within the foundation. This can lead to serious damage to the foundation itself, especially if the trapped water freezes. If the area that's leaking is small, then adding waterproofing to the outside is practical as long as you do not have to dig down too deeply. If you find areas where the mortar has failed, you can repair it. You can also add a waterproof membrane to the outside. This can be as simple as 6 mil poly sheeting attached to the foundation and sloped away from it. One caution: I am not a fan of digging around old foundations unless it's absolutely necessary. Disturbing the soil which has settled over a century or so may make things worse rather than better. If the amount of water entering your cellar is minor, it may be best to let things be. You could also try putting moth balls in the tunnels (to discourage further digging), then fill them in away from the foundation.

Your leak looks to be coming from the old metal (galvanized?) plumbing left in the wall. Your proposal is a band-aid, not a fix. Not even sure if it's code-legal; maybe a pro can chime in on that. I think your best long-term option is to open the back cabinet/wall, install new plastic DWV piping from your sink down into the basement and Fernco couple the new plastic piping to the existing metal vent pipe.

If you cannot get the stem out and replace internal parts, replace the entire spigot, or call the plumber to do that for you.