Don't use the same AP for both purposes
These are two very different use cases: a high-bandwidth, omnidirectional network for near the house, and a low-bandwidth, directional network for the shed. You'll be much better served by using two separate access points.
House: Ubiquiti U6 Enterprise - $279
As far as I'm aware, there are currently no Wi-Fi 6 compatible DD-WRT access points/routers. I'm also not aware of any outdoor rated Wi-Fi 5 access points that are DD-WRT compatible. You could definitely still go with an indoor DD-WRT compatible access point, but I think there are better options.
I'm recommending the Ubiquiti U6 Enterprise, since it's powerful with good coverage, supports Wi-Fi 6, is relatively easy to manage, isn't insanely expensive, and most importantly is IP65 rated so you can mount it outside (though I'd still put it under cover.) That said, if you don't like Ubiquiti there's plenty of other valid options; something from Ruckus or Aruba might be good, though likely more expensive. You could also use multiple inexpensive access points from someone like TP-Link.
Shed: Cambium Networks PTP 450 900 MHz - $139 (used)
Since it seems like you don't need a ton of bandwidth, but do need a lot of range and (more importantly) need to go through a lot of trees, I think a lower-frequency radio makes sense. Cambium is basically the only remaining manufacturer for 900 MHz radios (Ubiquiti used to make them, but no longer does.) You'll need one at each end, but given that budget doesn't seem to be a huge deal and these are fairly affordable used, I think it's a good strategy.
You may also want to add Yagi directional antennas for better signal strength. Cambium makes a 12 dBi antenna (the N009045D003A - $100), but you could use any 900 MHz Yagi antenna.