I have a finished basement with a storage room that has no flooring (just concrete)
There is a French drain, and all downspouts direct away from the house. I noticed some small heaving in this area pictured. It is clear that there is efflorescence as well. At this point what can I even do here? I can easily cut out a 4x4 section, dig down a bit and re-fill, but I dont know if that will solve it. Some of the basement slab is very thin due to the age of the house.
Hate to be the bearer of bad news here, but I've found that trying to keep moisture contained with concrete or fillers is a fool's errand. I've owned a 1911 house in Seattle for years and fought this a ton with a slab that is not consistently 4". Yes, you could cut it out, clean and coat the edges with a sealant then pour a new 4" block in. However, that's a ton of work and will likely just end up looking like a more geometric version of what you have already.
In my situation, I ended up busting up about 1/3" of my slab, shaping the clay underneath to all slope towards a new sump pit then backfilled it with 2 yards of pea gravel before repouring 109 bags of concrete. Dramatic and a mountain of work but even on the wettest January day in Seattle, my floor is dry.
Like you've probably heard, water intrusion is always a function of what's happening outside and a project for there, not inside.
That efflorescence could have taken a decade to form so I wouldn't be too worried about it honestly unless it's visibly damp or moist. If your slab looks like this, my guess is that there are far more important things to be tending to on your house. Sand or grind it real good, slap some paint on there and just monitor it once a season.
Sorry I couldn't offer any relatively easy solutions!
