tpm2-tools | The source repository for the Trusted Platform Module (TPM20) tools

Indeed. If a TPM2.0 Session is active, loaded in the TPM and in use, then you would see it in the list of TPM_HT_LOADED_SESSION.

Because the "tss2-software" stack stores the context in a file outside the TPM by default, then you would not see that session in loaded.

You would find it only in saved, when asking TPM2_GetCapability for TPM_HT_SAVED_SESSION as you did in your example.

Does this answer your question?

ps: Typically, context saving is needed when you have multiple users or applications working with the TPM. So, I am curious, is there a particular reason you want to use context saving or observe loaded sessions?

First you would take ownership with tpm2_takeownership. This gives you the hierarchy passwords you will need later on.

Then you would create the endorsement key with tpm2_createek.

Then you would create the storage root key with tpm2_createprimary, under TPM_RH_OWNER. Then you would make the SRK persistent with tpm2_evictcontrol.

It is not clear what you mean by loading the certificate to the TPM... But if you mean signing a key certificate by a root CA and storing it in the TPM, then you would store it in NV RAM and make it persistent (again with tpm2_evictcontrol) at the appropriate index handle (for example, in accordance with the TCG guidance).