We have identified the issue and a hotfix will be available in about four hours. Thanks for your help.
This workaround should work for you until the hotfix is out:
Go to /Steam/steamapps/common/Eco/Eco_Data/Server/Storage and rename the .db and .eco file of the savegame you are currently playing to Game.db and Game.eco (note the capitalization!) respectively.
Then start the server manually via the EcoServer.exe (in /Steam/steamapps/common/Eco/Eco_Data/Server/). You will then be able to start the game and in Your Worlds, at "LAN Servers" you should be able to join it.
Alternatively you can link your Steam account to an SLG account on
https://play.eco, that will solve it without the steps above being necessary.