What are some ideas or strategies you have to increase your org-wide influence as a CIO next year?

well, this sounds absolutely crazy but it will work like best.

we all are in the middle of transition of the way we used to work.
From one side, people have fear of AI and other side business want to implement AI ( they event don't know how)

when things are in super choatic, then calmness and going to basics help.
Just be supporter to your employees and be a leader for your board.

The theory:
There are some components of influence:
- Awareness: how many people know you
- Criticability: how much is organization suffering if you disappear
- Perceived competence: how others see you professionally
- Personal image: how others perceive you as a person
The practice:
I would advice (building on what Cristina Carnero said before me): 1. strengtehining relatioships with everybody (others C's are critical but not enough), consider everybody as your customer, 2. Create stories that includes your customers (continuous internal sale of your team and services). Promote and protect your team - the small talk of others is a very strong channel of informal info. 3.- "positioning IT as a business partner not a service desk, changing every IT initiative into business language" ( can't saying better myself :) ).
I would add: Pay attention to early signs - an unsatisfied user , a (business) pain not treated - do they have the potential to evolve into phenomena? Are they a tip of an iceberg?
If you also want power you have to add sanction capabilities, create regulations in your favor. I.e. shadow IT is eroding your influence and adds to the risks of the organization - eliminate it.
Remember to make sales _only_ on your the value your team is able to add.

1.- strengtehining relatioships with the other C's 2.- building a 12 months 12 CIO storytelling (people follow stories more than strageties) 3.- positioning IT as a business partner not a service desk, changing every IT initiative into business language (for instance presenting IT roadmaps framed by business outcomes not technology)