I messed around with wanting 3D backgrounds. However, I have zero desire to DIY. Most of the nicer premade options are mad of a rubberlike material, They liik great,m are easy to cut to size if needed. They can even be put into a going tank without moving the fish out. They can be silicaoned to the glass or not as one prefers.
https://www.universalrocks.com/fish/backgrounds
Juwel also makes 3Dbackgrounds.
One advantage to the premade flexible backgrounds is they will easily go into a tank with a braced top frame.You just rool or fold them and then open them ince in the tank. There is a lot of work doing this with styro based as you cannot fold or bend the pieces. So you must make smaller pieces that get joined one in the tank.
Year back I did a terraced tank using styro. You have to weight it down and perhaps even glue it to the class. Here is what I did:
The is a styro base under the upper terrace as well. For the big styro you see I hollowed it out from the back so I could insert a chunk of slate to help weight it. There was silicone used to help glue the styro to the back and bottom glass. After a slight rearrange this is what I got.
This tank was my high tech planted tank with pressurized CO2. it went through several incarnations over its decade long existence. When I decided it was to much work and repurposed it, they styro was still intact when I removed the terraces. So i know styro can live submerged as long as it is glued and or weighted.
I am not poor so I can normally afford to buy tank equipment rather than doing DIY. I reserve this for the things I cannot buy. However, there is very little one can DIY for less let alone as much as it would cost pre-made. The reason is one's time has value. Aside from the pleasure of doing it oneself, the cost is almost always greater. You can likely do a bit of part time work for a number of hours that will earn you enough to buy it pre-built than the number of hours it will take you to make it yourself. Your time has to be worth at least $15 or $20 an hour at worst.
FYI- I spend the better part of the summer doing the design of the above tank and then making the rock walls and styro bases in the pic. I would bet I had well over 100 hours in the project. But for me there were two factors involved. The first is I could not find the above pre-made, so DIY was the only option. I did this over 20 years ago and even if I could have found this pre-made, I could not afford to spend what it would have cost. But at just $10 at hour for my time, it took well over $1,000 to make it. My time is worth more than that
All this said, I wish you good luck with the project. It will not be easy and it takes some artisitic skill to make it come out looking nice. But if you are happy with the final product you create, then it will be worth it in satisfaction.