Quoted from Rando:
Disclaimer: I don't know anything about plumbing.
Couple of my houses in NJ has sump pits and sump pumps (I don't see a pump in your pics). Water in the pit was normal, and when it exceeded a certain level the sump pump would kick on to drive the water out. After installing flooring, we had a lot of rain and the pump blew the circuit and flooded the basement and I had to replace the flooring again. Resolution:
1) Replaced original pump
2) Replaced circuit
3) Added secondary pump with battery backup
4) Eventually added house generator that kicked on automatically with loss of power
Don't fool around with water in your basement, luck!
I added a second battery backup pump in our old home outside of Philly... same reason. We had a massive storm, power got knocked out for more than a day, and the basement flooded.
A whole-home generator makes sense. But, the battery back up is way more affordable... but, OP, if you're thinking about finishing your basement and there's evidence of water, definitely throw in some sort of secondary system. You might never need it, but if you do, you'll be REALLY glad you have it.