Check to see if the house roof is pitched toward these walls and whether it has gutters in place. If water is being dumped there off the roof during a rain, and there's nothing being done to lead it away from the house, then adding gutters should fix the problem.

Indoor swimming pools are a problem. Water management begins on the exterior, not the interior after its arrived. If the slope is towards the house, that regrading needs to be addressed before ever moving in. With a substantial escrow from the seller to pay for it.

If you had asked this question a month ago, I would have probably said, it didnt look terrible after 4 days of rain, and if you get good reports, I would probably buy it, but, after dealing with storm damage, that badly damaged my roof, and caused water leakage in several places in my house, that have kept me occupied for more than a month, even though, I am about finished with it all now, I would probably not buy it. You can take this answer with a grain of salt, from someone who is old, and tired of being on ladders, and tired of repairing. I am fixing the last spot today. LOL

In my, there is no such as a truly dry basement so I don’t think it’s a big deal. I would never finish a basement because of the dampness.

This is incredibly common in older homes in my area. All new homes have drain tile and sump pumps. Our home is an older home with a finished basement, with drain tile and a sump pump. even with that, we got water in one corner of our storage area after we moved in. We had Landscaper regrade our yard and haven't had a problem since.
all this to say, at least in my area, this would not be a deal breaker.

This is old concrete block, not poured, foundation, the walls are damp, and there is standing water despite a sump pump. I say run, don’t walk, from this one. You can do better.

A bone-dry basement in an older home is rare. I've owned four homes with basements and they've all had problems. As mentioned by others, there are methods to reduce moisture infiltration. What are these anchors you mention?

I looked at the picture again and there are several things that concern me. The two walls are made of different materials. The concrete block side appears fine. The other wall that appears to have for lack of a better term glazed tiles has problems. Although the company may have placed anchors which are normal to keep a wall from buckling it does not appear that they did anything to stop water seepage. If you look straight down from the anchor on the left you will see that the seams appear damp. With the raised edge of the sump pump any water would need to be that high before it could be pumped out. Any thing that you would put in that basement would need to be raised above that level. Having had my basement flooded by a 13+ inch rain I would pass on this house because of the way the sump pump is installed. I would be too concerned that the anchors were also wonky.

"The seller disclosed that during heavy rain there is sometimes “water seepage” on the south facing basement wall."

Yeah, that to me appears to be considerably more water than "seepage".......................

It's an issue. It doesn't mean that it's insurmountable, but it's an issue.

This is very common with homes built with concrete block foundations. Your problem is on the outside wall. Chances are there is no drain tile system installed at the base of the foundation. If there is one, it may be blocked by sediment and unable to drain properly. That means digging around the perimeter of the house and installing a drain tile system. It's messy and expensive, but it can be installed or repaired. The interior wall can be painted with an anti-leak substance, but it only works of pinpoint types of leaks. It's not a solution to the bigger issues.

The second issue to look at is the guttering system of the house. Do the gutters work? Are they dumping away from the foundation? They may be inadequate for the roof. You may need more downspouts or the current ones rehung to slope properly. The downspout may need to be extended away from the foundation. This is not difficult to fix, but it costs money. Even if they are dumping into the corner, the foundation will still need attention.

Last, what is the slope of the land in relation to the house? Does the land slope away from the foundation? Is storm water being run towards the house? This problem is almost impossible to fix, is very expensive and I'd walk away from the house.

Do your trust that sump pump to run when you need it to run? How old is the pump? How often does it run? Do you have an alarm on it? Does the house lose power frequently? Do you have a generator?

Answer all of those questions to your satisfaction and you will know if the house is worth pursuing. Good luck.