When you try to insert a picture via the Home tab, Publisher attempts to open a dialog where you can choose both online and local options. I believe it is choking on trying to find the online options via a Bing search and/or from a cache of pictures you have saved to One-Drive.
If you want to insert a picture located on your computer or even a USB drive or other external hard drive, the better work flow is to go to the Insert tab > the Illustrations group and select Pictures there. Then you won't choke Publisher trying to make the internet connection. And the Online options are also available...
In my view you should never try to insert a picture directly from an online source to begin with. Best practices in my opinion is to always save that picture to your local hard drive and insert from there. That way you have a copy of the picture if you need to use it again, edit it before you insert it. Further you are far less likely to corrupt the picture or the Publisher publication by trying to insert directly from the internet source.
If you insist on inserting pictures directly from OneDrive then this article may be helpful in resolving the problem you are having.
Insert Online Picture or Video: https://support.microsoft.com/en-us/office/unable-to-access-onedrive-from-insert-online-picture-or-video-265e1fed-7e61-4a22-b8ff-52c1dccc101d?ui=en-us&rs=en-us&ad=us
DavidF