Water – Is this hole at the corner of the foundation major issue

I would definitely be concerned, mostly about mold but also about property damage (you said it's used for storage) and long-term foundation damage.

If your downspouts are not properly discharging water away from your house then you definitely want to address this. In the grand scheme of wet basement solutions, this is probably the cheapest fix you will find. Tight property lines or not, make sure that your downspouts discharge water far away from your foundation. It's hard to say whether you would benefit from a dry well.

If this fails then you should investigate whether you have a French drain and/or weeping tiles and whether that system has failed. If it is just clogged it could be a somewhat easy repair. If you don't have one or it has failed beyond repair then you will need to install or replace the drainage system. You said your house has tight property lines so it might not be realistic to dig up the outside, in which case you'd have to look into an interior French drain and sump pit solution. Either way this is probably going to be expensive.

I would definitely advise you to bring an expert in to review your situation and suggest some solutions. Make sure to get a few opinions/quotes. Fixing this this is probably outside of the DIY-scope for most people as messing with your foundation is risky business.

This time of year is prime for water seepage into unsealed foundations. With water tables on the rise and the top of the ground still frozen, there tends to be less natural drainage and a bit more water pressure on foundations. This is also a bed time of year in northern climates to improve external drainage. A good drain tile around the foundation directed away from the building or a sump pit pumping water away from the house is the usual method. Since that is not your best option now, the other option is to treat the interior of the foundation with a hydrolic sealant like DriLoc. Driloc and products like it are applied like paint to masonry surfaces and will protect against leaking for up to 4 or 5 PSI external water pressure. The external pressure of ground water against the walls is usually very low, under 2 PSI, so this product is very effective. The only problem is that the surface should be dry when you apply it. You may have to suffer through the current situation for a bit until the surface can be dried. When you do apply Driloc, it is important to clean the surface well, remove any and all efforant mineral deposits, old paint etc. When applying the product, work it into all the tiny holes of the masonry. Pay special attention to joints between walls and floors. Two coats is normally necessary.