Welcome to Microsoft Q&A!
How can I use the trusted certificate with the different subject from Package/Identity/Publisher to create a side load and store app which resolve to the same package name so that they are considered the same application?
No, this is not possible.
There is something that needs to be clarified. UWP apps need to be signed with a certificate so that they could be sideloaded or uploaded to the store. If you want to upload your app to the store, the store will sign the app with the certificate that matches the developer account you used. That's why the store rejects your app because you are using a different signing certificate.
Also, if your app is uploaded to the store with your developer account, and you sideloaded your app with another certificate, both of the apps will exist in the system because the system will consider them as two different apps.
Another thing is that may I know why you purchased a certificate instead of using your own certificate?