well, usually that's what causes a flood area, it's a bowl, but even if I span outwards to the sides, all the land is higher than the bowl area so I can't simply just put catch basins and underground pipes over to the sides and then 90 degrees and straight out to the gutter.

I want to plant Magnolias and Nootka Cypress along the back and back side fences. But wet feet, even if it doesn't kill them, usually with a hurricane there's lots of rain so the combo of flooded roots and high winds = can windthrow easier, there's not much in the way if these trees ever do fall even at their supposed max heights of around 40 ft, although there's lots of contradictory height estimates for most species and I don't want anything gigantic that can fall on a house but 40 ft would be fine and not do any serious damage except maybe some fence and shed(s) and these don't branch outward with large limbs like an oak or maple.

Anyway, in the center where it says Pool is the worst area, it floods about 5 inches deep there, and it doesn't drain away for over a week sometimes. Unless it's warm and sunny, I think the water eventually just seeps down and towards the house foundation which can eat away at the 3.5 foot deep cinderblock foundation , no basement here though.
A few Blue Point Junipers did fine with wet feet there for many years but were near their end of lifespan, only lives about 40 years and got scraggly etc and were chopped out, then emerald green arborvitaes replaced them and they did fine for several years with wet feet too but this past drought heat wave summer killed them so I'm replacing them with magnolias and nootka and maybe some other mid-height evergreens.

So back to the flood, there's a house behind, I think this yard is slightly down hill from that, and both sides, so I can't direct the water that way.

Is the only real way to get this water away is by picking a back corner and making that the high spot and then bringing in a lot of dirt and making the whole back a slight ramp from left to right, and then ramping it down to the street?

The high point might need to be quite a bit of build up because it needs to be higher than the gutter - I think the back sides sit only slightly higher than the gutter, so to have the water shed down to the street or to install drainage pipes would need to be higher.

I know there's pump setups I've seen on youtube from well experienced drainage companies and they can freeze but had installed heater tape in them which is basically not to code I don't think plus is just a headache with parts etc I don't think anyone will maintain and will eventually become a problem.

BTW, the back left side stays wet underground a lot, it turns out according to historic aerials, a Google earth type site that goes back to the 30s and before the development was built, that there was a man made drainage channel right where they built this house, it actually still shows a blue line on google maps there as if there's a river, I've dug fence posts out when it hadn't rained for weeks and a few feet down I hit pooling water, It all comes down from about a mile away there's a rather large hill that this is all down grade from, I don't think there's any concrete tubes/channels that make a river under there or anything, I think it's something like sandy soil over top of very clay soil that allows rain from uphill to saturate this area, So since the back left already has this issue I can't do anything about, maybe it'd be best to slope/run this pool flood from right to left and into the already saturated area but also hopefully to the gutter in the end.