It is possible but not for all the properties, depending on the version of Office Client you are using and if the columns can be recognized by SharePoint.
Most properties in the word document can be synced to SharePoint library as long as you have a corresponding column set in SharePoint. It can either be set the document content type, or the library itself.
Some properties in the screenshot you provide are available with default columns in SharePoint: Title, Comments, Status, Categories, Subject, Author.
Some properties have columns with same or similar names in SharePoint, but they are not recognized: Company, Manager.
And the rest of them cannot be synced even if we manually create a column in SharePoint.
There is currently no manual way to map the properties to SharePoint. So if you want to managed properties in the word document, it is better to use SharePoint properties instead, since they are more clear to easily added or removed from SharePoint side.
In addition, I’m using Microsoft 365 Apps for enterprise to come up with the test results.
There is no built-in approach to actually map the properties since we cannot change the communication method between these two products. What you are looking for is a way to update the corresponding properties while uploading.
In fact, you can create custom properties for every individual document via
Properties > Advanced Properties > Custom, and the properties listed in the Properties list will be synced to SharePoint, as long as you have a corresponding column (same name and type) created in the library.
Please note that this works for the current document only, so it is not a solution to your question.
Reference: View or change the properties for an Office file.