Okay, so 2 vastly different builds here

.
The "Forex" Build:
More common in the EU, than the US, very very expensive, but will last, pretty much forever.
You build a frame, that will hold 1/4 thick panels, with this.
https://eztube.com/product-category/tubes/aluminum-extrusions/
While doing so, I wouldn't trust a 8ft panel, or even 6'/7' in the back, so run a cross beam down the center of the cage area in the back, where you can use 2 panels.
I would use 2 pieces of HDPE as the bottom, or even better 1/2" piece, with a route cut in to go around the groove.
The frame has sliding glass door track options, so that is also covered

. I would get some Nylon Slips that sit into the track for the doors to slide. I ran into that, with my cage. I got Alu track, and the glass doors did not want to slide easily, I have since found better tracks with the slips, but I think you can buy the slip material. So on the sliding door track, plan to use the "top track" on both top and bottom, and find a Nylon slip that will cut the height in half for the bottom one and allow the doors to slide.
The "Wood" Build:
Easy, just like building a cabinet. Couple sheets of Plywood, and maybe some framing as this is pretty large. 1x3 framing would likely be sufficient, 1x4s if your worried.
To seal it, you got a few good options. I would go with one of these,
Marine Expoxy: LONG curing/off gassing time, longest lasting, sturdiest,
Sweetwater Epoxy: Semi short Medium Curing/Off gassing time, designed for Plywood Aquariums so 100% safe after the directed time frames
Pond Armor: Really short off gassing time, contains no VOCs, very thick and hard to work with, but can be thinned (with VOCs lol) Touted as fish safe for Koi Ponds, so again safe quickly. Semi rubbery when dry, so less prone to stress cracks, than the other 2, still can/will crack.
All of above will stress crack on subpar seams. So you need to ensure rigidity in the seams, and then its helpful to use Fiberglass Matte, or Cloth in them and use your chosen product as the Resin. This will add strength and rigidity to the seams as well, which is especially good for the soil bin.
I seen your pond liner bottom idea, Id scrap that for Flex seal, and you can flex seal the soil bin after you sealed with above methods as well as a extra JIC. The issue with pond liner is, it has to be mechanically fastened and water can and will get in between the liner and the water, unless its glued in very well with like contact cement, by the time you did