The “Network or server error” message is a generic catchall error message, so it doesn’t necessarily mean you do not have a connection to the SmartThings cloud.
As mentioned by @jkp it’s possible you could be hitting the limits, but your existing Automations would have to contain a lot of actions (“behaviors”) per each Automation for that to be the case. If you have a larger Automation such as an “All Off” type, you could try temporarily removing that to see if this is the case.
I would especially consider the above if you cannot create any Automation regardless of type (scheduled, device triggered, location/mode triggered, etc.) or devices in use. If you have not experimented with what Automations you can or cannot create, give a few different kinds and devices a try to see if you can identify where the error might be coming from.