I was going to say “no big deal” until you said there was moisture showing on the wall itself.
Clairmont houses were built w/o a stucco screed and it seems the general plan was to let the water run up against the house before continuing out to the street. All of our concrete was sloped to the house util we had it redone.
If the outside concrete is below the stemwall, then it isn’t as bad, but it is still a problem. If you have too much moisture in contact w/ concrete, the concrete will eventually start to deteriorate. You will see the concrete turn to white powder and start falling apart.
We didn’t have the stucco scraped to install a screed, but we did slope the concrete away from the house and that works well. The eves/gutters and the slope keep water away from the house enough that we don’t have moisture in the stucco.
However, we still have some issues where there is no concrete – i.e. where dirt butts up against the stucco with no screed we still have some issues w/ the stucco turning to powder.
To summarize – If you only have concrete sidewalks in contact w/ the house, I’d slope the concrete and get gutters. If there is dirt up against the house, then you should probably do all three: slope the concrete, put in gutters, and scrape the lower stucco layers and have a screed put in. Of course, matching stucco colors is not fun and you may end up puting a color layer on the whole house.