@Chiad I should preface this by saying that Vintagestory on the SteamDeck is installed as a flatpack which I don't think are usually intended to be modified after they're built, so I'm not sure about the permanence of this solution. This might be a good long term solution or you may need to reapply it occasionally after updates. Also, this is going to require a bit of typing, so you may want to connect a mouse and keyboard.
With that out of the way, to find the file in question, you'll need to press the STEAM button on your deck, select Power, press A, select Switch to Desktop, and press A again. Now that you're on the desktop, grab out your trusty mouse and keyboard, open the app menu by clicking on the SteamDeck icon or pressing the Windows key on your keyboard then search for konsole and launch it. Now that you're at the terminal the file in questions seems to be located at /home/deck/.var/app/at.vintagestory.VintageStory/config/VintagestoryData/clientsettings.json. If you're comfortable using terminal based editors and I'm going into way too much detail, then you've probably got it from here and can use your preferred editor to make the change. If not, rather than explain how to use nano or vim (lookup how to exit vim first lest you become trapped), it'll be easier to just copy the sed script below into your konsole window and press enter.
sed -i -E 's/"webRequestTimeout": [0-9]+/"webRequestTimeout": 30/' /home/deck/.var/app/at.vintagestory.VintageStory/config/VintagestoryData/clientsettings.json
This inline sed script searches the config file for the line "webRequestTimeout": <any number> and replaces it with "webRequestTimeout": 30. You can replace the 30 with any value you'd like to tune the timeout to something that works for your connection speed. You can also run this script as many times as you like and it will simply update the timeout to whatever you replace the 30 with. After each change you can run the following to verify that the value was updated correctly.
grep "webRequestTimeout" /home/deck/.var/app/at.vintagestory.VintageStory/config/VintagestoryData/clientsettings.json
If all went well, you should get some output that looks like this
"webRequestTimeout": 30,
This indicates that the field was updated correctly. Restart vintagestory if it's already running and then try checking the server list again. Please let me know if any of this is unclear or if you have any questions but hopefully this helps. Good luck