WorldDownloader VS SeedCracker

Earlier minecraft versions had World Downloader, but I haven't found anything similar for 1.18+.

World Downloader MOD

Yes it is possible. You'll need the World Downloader Mod, or WDL for short. WDL can be found here.

In case you didn’t see the link OP: https://www.minecraftforum.net/forums/mapping-and-modding-java-edition/minecraft-mods/2520465-world-downloader-mod-create-backups-of-your-builds

if u need a world downloader mod, here it is. This is only updated to 1.16, so it won't work on 1.17 clients. other than that, you can always grab the region files for the server if they allow you to

Are you still able to access the server? Try this mod which let's you download any world from a server.

worlddownloader mod, i think the link is https://github.com/Pokechu22/WorldDownloader

(just scroll down and download the file called WorldDownloader-forge-4.1.0.2-mc1.16.3.jar) and lauch it with forge

If you don't respect this, you can use https://github.com/KaptainWutax/SeedCracker

Custom code, usually. KaptainWutax made a program a few years ago which can crack seeds just by scanning the world. When seed cracking, though, you are looking for certain features which can rule out many many seeds very easily. For example, finding specific dungeon coordinates and mossy cobble patterns can narrow it down dramatically. For this process, you need not scan that much since it's some simple maths applied to not that many blocks and not checking very many times.

Im not an expert but cords are needed or at least if you want to solve it in any time. you say you play on that SMP so maybe use seedcrackermod but KaptainWutax. It is a fabric mod that searches the world for structures like shipwrecks and once you find 5 of them it can crack the seed within minutes or even less (depends on your gpu)

Otherwise, I found a mod that will calculate a server's seed but you have to actually be on the server; most of the actual tools seem to be private, most likely due to security concerns as stated above.