Wet spot on outside of foundation oozing

The fact that the water is seen in the pit only after a rain is a good thing, meaning your water table is not the problem, because that would mean a sump pump for sure. I think you are just seeing this because the valve is only 2' from the wall. Normally, it was dissipating. You had a good wall/slab system that wasn't leaking until a hole got poked in the slab for the repair

Some grading of the soil alongside this wall for better runoff might be in order. Any drainspouts nearby?

Some ad-hoc pump automation in the pit would give you some peace of mind until you can get outside for some landscaping.

Self contained sump pump

To verify gutters-to-storm drain are intact and not leaking down at the slab level,
Put a bottle of easter egg dye into the storm drain connection. If you see the color in the pit, I would disconnect the downspouts and direct them into the yard.

A pain for mowing, but the flip up ones work well. In our area, downspouts were connected into the floor drains and thence to the sewer. In the 1990s, we had to cap the connection with concrete or face a fine.

OK, the water must be coming from somewhere:

1. Water from a leak. If you've been checking your meter and don't think you have any leaks inside that's good, but it's possible there is a crack or break in service line upstream of your meter. This might actually explain reduced water pressure in the house. If you suspect this is the problem I would call your water company and have them take a look.

2. Rainwater. If the water appears only during and shortly after a storm, then you probably have a drainage problem. Make sure all gutters are directed away from the house. You might also look at grading near the house to make sure water will flow away from the house. Is the porch at the bottom of a slope towards the house?

3. Groundwater. I would be a little surprised if this were groundwater welling up, but it's not impossible. Have you had a very wet spring that would've raised the water table level? Or done any serious landscaping / excavation / compacting in your area?

4. Septic system. An unhappy septic system can cause water to well up, although probably not so close to the house or clear / odorless. Do you have a septic system?

(I wouldn't beat yourself up too much about not sealing that gap. If water is pooling from below I doubt a little sealant would hold it off for long.)