If the Prophet said:
Verily the family of Ibrahim were possessors of the authority given from God, who believed in their leadership and did good was in paradise, and who turned away from it were in hell. O humanity, do not envy people for what God has given them out of his grace just as the family of Ibrahim was envied. O you who believe obey me and obey those who possess the authority from you so that if I command you to war, then you must go to war. Indeed all Messengers were sent so that they be obeyed by God's permission. Who obeys me, indeed obeys God.
I would say given the context of the family of Ibrahim.
1] Their authority is one and the same.
2] It's primarily emphasizing on religious and spiritual authority, but includes political authority.
3] The "so" if he commands us to war, shows not only an aspect of authority of the Prophet, but obviously that of the possessors of the authority.
4] The emphasis on the family of Ibrahim before the verse while emphasizing on obedience to all Prophets after, show both that their authority is one and the same to that of Prophets while at the same time, they being a chosen family themselves [ie. that Mohammad has an exalted chosen family likewise who are divine authorities]
Now we see emphasis on the great authority of the family of Ibrahim in 4:54. 4:55-56 warns against turning against such authority. 4:59 commands to towards possessors of the authority from the believing nation of Mohammad. The verses after 4:59 are emphasizing the particular emphasis that part of the obedience towards the Messenger is to refer disputes back to Him and without that they don't have faith.4:69 then emphasizes that all Messengers were sent to be obeyed by God's permission.
In other words, the context of the obedience here before and after, is that of the Prophet's authority. That of the authority of the family of Ibrahim. The authority of all Messengers. It's not talking about anything else.
Also, if I say
"Eat fruits and vegetables therefore eat the apples and the oranges."
Or
If I say
"Listen to your teachers so if Mr. Fleming assigns you homework then make sure to do it"
Neither of these statements mean you don't do the first command but rather are just emphasizing on a particular instance of that command.
For example, it can Mr. Fleming is the main teacher of this person at that time, so I am emphasizing to listen to that teacher and do what he says.
However, it means to obey all teachers in that fashion as well, however, Mr. Fleming being the main teacher of that time, it's not against norm of language to particularly emphasize on a particular to instance of the the general command.
The same is true of verse 4:59. It could of said "wa laken" (but if), but it didn't. In other places in Quran, it does use those words for "but if".