You are running Aurea Social within SharePoint 2010 and encounter an issue where you cannot use the Add Web part feature in Google Chrome or Microsoft Edge. Selecting the Add a Web part button when editing a page does not result in the "Web Part Selector" ribbon menu appearing. You have verified that this is working on Internet Explorer.
This behavior is not within the scope of Aurea Support, as this is a problem with Sharepoint directly. You can reach out to Microsoft support for help with reviewing this specific behavior in more detail.
Please note that Sharepoint 2010 support ended on April 2021, as detailed in the following Microsoft article. Our recommendation is to upgrade your Sharepoint version to a supported one. Our latest Skyvera versions support Sharepoint 2013 and 2016.
As a potential workaround, you can review this article from Microsoft, which details the steps for adding Web Parts within 2010 via the Insert ribbon menu.