Sorry, I disagree. Tar paper is permeable. Here is one of many links on the subject
A giant sinkhole is about to open up underneath this house and swallow it whole. I would seek at least 1/2 price reduction from the seller.
Looks like they didn’t grind down the surface patching material including the injection ports. Not much you can say at this point, other than note the wall does not appear to have moved since the cracks were filled. Foundation movement typically takes years of gradual movement, so the missing link is when did they first appear and when were the cracks filled. Typically most cracks get filled when they leak. Polyurethane is better at sealing wet cracks and epoxy provides some strength, but needs dust free dry concrete to adhere properly. Soil type, how drainage was managed over the years, soil compaction under the footings and reinforcing steel in the concrete all contribute to foundation movement. Your odds at predicting the exact cause is like winning the lottery, so it’s best not to speculate on the cause, just report what you see.
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This is not a home inspector.
Then you get what you see.