This is a classic symptom of a broken bridge between two Microsoft tools that were designed to work together. The error "Cannot connect to the server at this time" is almost never a transient network glitch; it is almost always a permissions or authentication mismatch that Excel refuses to resolve gracefully.
The user in this case has confirmed they can manually add items to the SharePoint list. That means their account has the necessary write permissions on the destination. The problem, then, is not whether they *can* write, but whether the Excel export wizard can *authenticate* correctly through the modern browser stack. The old workarounds involving Internet Explorer are dead, and that is a good thing. But Microsoft has not provided a clean replacement path for this specific workflow. The export feature relies on a legacy authentication handshake that modern browsers and security policies often block by default. The user is caught between a tool that assumes a simpler security model and an IT environment that has rightly moved on.
What this means for you is practical and frustrating: you cannot trust the built-in export-to-SharePoint function as a reliable workflow. If you need to move table data from Excel to a SharePoint list, you have better options. Use Power Automate to create a flow that reads the Excel table and writes rows to the list. Or open the SharePoint list in Datasheet view and copy-paste directly. These methods bypass the broken authentication layer that the export dialog depends on. They are not as one-click convenient, but they will not leave you staring at a dialog that says "cannot connect" when you know you have access.
The deeper takeaway here is that Microsoft has left a dead feature alive in the interface. The Export to SharePoint button should either work reliably or be removed. Leaving it in place with a vague error message wastes user time and erodes trust. Do not waste time debugging a connection that your security team has already killed. Move to a modern integration method. That is the only fix that will hold.