Hi @john john
You can refer to following steps to configure elevated privileges
https://learn.microsoft.com/en-us/sharepoint/dev/solution-guidance/elevated-privileges-in-sharepoint-add-ins
For the difference between rest api and CSOM
Developers can perform Create, Read, Update, and Delete (CRUD) operations from their SharePoint Add-ins, solutions, and client applications, using REST web technologies and standard Open Data Protocol (OData) syntax. Here is a document for more details about rest api
https://learn.microsoft.com/en-us/sharepoint/dev/sp-add-ins/complete-basic-operations-using-sharepoint-rest-endpoints
The CSOM internally uses the PSI services, the CSOM has many of the same functional limitations that the PSI has. In addition to limitations of the PSI, such as having no access to data in local projects (.mpp files), the CSOM does not include administrative functionality that Project Web App typically handles. For example, creating custom security groups can be handled in the Site Settings - Permissions page for Project Web App. See the What the CSOM does and does not do section in the document
https://learn.microsoft.com/en-us/office/client-developer/project/what-the-csom-does-and-does-not-do
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