Hi @Otto Vannetelbosch (Admin),
Thank you for posting in this community.
Since we can't reproduce your situation, we need to narrow down the problem and try some things.
1.If your SharePoint Designer is not recently installed, I suggest you uninstall it and redownload SharePoint Designer. SharePoint Designer may be updated. Here is the download link for SharePoint Designer 2013: Download SharePoint Designer 2013.
After installing SharePoint Designer 013, test to see if you can open site from SharePoint Designer.
2.Kindly check if other Admins cannot sign into SharePoint Designer. If other admins are having the same behavior, kindly check if legacy authentication is enabled by using SharePoint Online Management Shell. If you are new to SharePoint Online Management Shell, you can refer this article to get a quick start: Get started with SharePoint Online Management Shell.
Connect-SPOService -URL https://domain-admin.sharepoint.com #Please enter your own admin site collection
Set-SPOTenant -LegacyAuthProtocolsEnabled $True
After 3.If Legacy Authentication is enabled but still having the same behavior, you could try to Enable Modern authentication for SharePoint Designer.
You can also refer to this thread to enable Modern authentication for SharePoint Designer: Error "Your account is in bad state.Please sign-in to this account online to address the issue" while opening Sharepoint Online site in SharePoint Designer.
Please note that the version of Office you are using may be different from the one in this thread, you can download the DLLs for your version of Office from the web.
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