What is Shanks relationship with the Gorosei

It’s quite clear that Shanks has some knowledge of all the world old knowledge due to the fact he was on the Pirate King's ship. Even if he didn’t go to laugh tape. (btw Raftel is not the correct name of the last island per Oda himself. The final island is called laughtale or laugh-tell. Anyways.)

It’s very clear Shanks is there to either talk about Blackbeard or Luffy. The reason why is because Shanks is the symbol of maintaining balance between all the Great Powers. Unlike other yonko Shanks only fights to defend people he cares for and his crew. He is not actively seeking more power like Kaido, Blackbeard and Big Mom.

He would rather maintain things as is but, since he knows he can not stop the changes in the word Luffy has brought, he is most likely issuing a big warning to the government, possibly about Blackbeard doing more than what has ever been done in history.

Lots of theories claim Blackbeard is actually 3 people and Shanks could be warning them that because of what will happen in wano. It will lead to Blackbeard acquiring a third devil fruit or perhaps a road ponneglyph or ancient weapon.

There’s no such thing as Shanks being a double agent. He is too close to major pirates: Roger, Luffy, Rayleigh, bullet Buggy and many others. It’s not in Shanks' nature to be a disloyal person.

Short answer - We don't know canonically, as there is absolutely no information on the matter. All that follows is interpretation of their exchange when they meet.

Based on the few short panels of their interaction, we see the Gorosei mention:

"We are in the middle of the Reverie. A man with a position like yours isn't suitable to get involved in the world of politics. We only made time to talk because it was you."

At first thought, it will seem absurd that the position would refer to him being a Yonko, since the Marines are against them. Many theories have indeed surfaced that Shanks may have some other status that allies him with the Gorosei or makes him worthy to be treated in such a manner. In my view, it is very much against Shanks' character to be a double agent, given how it has developed. Below are some other technicalities to consider.

Firstly, the reason the Marines leave the Yonko alone to a large extent is due to their influence and ability to put up a big fight. They'd have to expend a lot to capture someone at the Yonko-level, which is not worth their efforts unless something major happens. Even in the two instances when Shanks was interacting with other Yonko (Whitebeard and Kaido), they merely attempted to stop the meet by blocking him, and did not attempt capture.

Secondly, the World Government and the Marines are separate. The Gorosei are under the WG, which has its own agendas beyond simply capturing pirates to maintain peace. The Marines fall under the WG, but so do multiple secret forces like the CP0.

In the very next chapter (908), we see the Gorosei mentioning that the "balance of the world cannot be maintained forever". All their appearances seem to indicate they choose to maintain the balance of the Three Great Powers (Marines, Warlords and Pirates), even though one would assume they'd be happy if all pirates were eliminated. Thus, there's definitely more than meets the eye.

Enough to guess that the Gorosei might not have any direct motivation to capture pirates (like the Marines), and definitely not those at Shanks' level.