You're not giving examples of how you are splitting yourself from your character and how you (the player) are not influencing the character. It's you (the player) making the decisions the whole time. The character only exists in your head.
If you decide to ask the DM, that's not character agency, that's you (the player) asking for an outside opinion just like it would be the player suggesting the character know a shortcut to the DM.
There is no split between character and player here.
Agency means 'capacity to act'. The first word is key. It indicates where the action is emanating from.
If I limit those actions to the scope of activity that lies in the character's purview then the character is the one acting and the scene is resolved with character agency. For example, running down an alleyway I know will get me closer to my target. For the player to make these choices sometimes requires additional information from regarding the scene. Asking if the character has particular knowledge is just asking for such a clarification. It does not commit the character to action and offers no effect on the game world other than resolving an uncertainty. How the the one in control of the scene chooses the answer is immaterial to me. It could be written down, it could be probability based, it could be at his whim.
If I do not limit those actions in such a way then I'm acting as a player. Some games have formal rules for such actions. In those systems, I am free to tell the GM that I know a shortcut and am gaining on the target. This may cost a player resource like a token, card play, or may grant the GM the ability to add a complication as he wishes depending on the game.
In some cases, I may be trying player agency less formally i.e. through negotiation ("Hey DM, wouldn't it be really neat if we caught him this way and got onto the main plot tonight?"), bribery ("Gee, I'm getting a bit hungry, what do you say I order us a pizza as soon as we catch this guy!", or extortion ("It'd be a shame a SHAME I say if that coke bottle were to tip aspill all over your cards!")
Regardless of formality or informality, I prefer to resolve situations within character agency.