Unfortunately, you can't "drain" into saturated soil. At that point you're building a boat more than a house: keeping water out on all sides.

I'm assuming it's a fully-enclosed basement? I.e. no walk-out side?

The best you can likely do is waterproofing the basement walls + pumping out from inside or an inside-perimeter drain. But that's only racing pump_out_flow > seep_in_flow.

And that's a bad game to be in, because water under pressure (which it will be a story below ground) finds a way.

I'd make the basement flood tolerant (limit mold-hosting materials and places water can be trapped) + pump it out quickly after it floods + buy a dehumidifier, and accept it's going to happen.

As far as I can tell inside waterproofing is a bad idea, it leaves your foundation soaking wet, excess humidity indoors, and as you point out it doesn't alleviate the pressure from outside. Waterproofing the exterior, french drains deeper than the footings (all sides), and sump pumps... That should keep things dry but it's quite a process.

Foundations being wet aren't a huge deal. Exterior is recommended over interior because it's easier to ensure no gaps. But it does involve substantial excavation.

French drains around the perimeter help, but you're literally fighting water from all directions... including directly underneath.

Have a perimeter French drain but a crack in the slab? Enjoy watching water bubble up from that crack once things get saturated.

Yeah it's not a cheap approach but unless the water is coming in really fast it'll get the basement really dry. Key to have the drain and pump well below the footings otherwise yes the water will just be under the slab.

The issue with drain/pump solution is that at that point you're doing hydrological engineering.

There isn't a "perimeter" per se, because water is literally coming from depth (in most locals / soil types).

So drain/pump just creates drier 3d soil areas. Whether that's enough to attract all the surrounding water (at a high enough rate) that would otherwise be infiltrating depends on soil permeability (e.g. sandy or clay?).

A lot of the "handyman"-type "dry basement" shops have no idea about any of this, toss a generic solution in there, and then blame the gods if it doesn't work (and they've billed for time-consuming and expensive excavation).

Ah true. I live in a hilly region so the water issues tend to be rain water moving down hill (which is really mostly laterally). In that situation the exterior drain solution works well, totally dry basement. I don't know how common it is for water in a populated area to be coming from directly below but in that situation maybe it's a good place not to have a basement.

Yup we have a dehumidifier running constantly that drains into the sump pit. The basement still has a basement smell even though it's all brand new drywall, fresh paint, etc. The dehumidifier keeps the humidity around 40%, otherwise it would be approaching 75-80%

Do you know if there's an impermeable barrier on the interior walls? And what foundation material behind the drywall?

It gets dicey applying internal barriers, because one needs to be thoughtful about making sure there's a place for water to go when it's actually too much (you don't want an internal barrier to be a dam holding back all the pressure), but it can be an option.

They sell them in membrane form or paint-type form.

Up here in Alaska, I tend to get a little water seeping into my basement at the cove joint (walls are ICF) after heavy rain and/or the spring thaw. Now, the floor in the basement is concrete, and whoever built the house had the baseboards and drywall over an inch off the floor, so towels and a de-humidifier tend to dry it out and nothing gets ruined since we learned to keep things off the floor. Trying to think of a way to address it without digging around the foundation to put in more/better drainage. Maybe just add a sump pump... I know, kind of a band-aid solution.