There are four routes into the Blue Zone: a government delegation, an admitted observer organisation, media accreditation, or the UN system itself. There is no way to buy a badge.
The observer route is the one most organisations use, and it is also the slowest: an organisation has to be admitted by the Conference of the Parties before it can nominate anyone, and that admission process takes years rather than months. If your organisation is not already admitted, the realistic path for 2026 is to be nominated by one that is.
Registration runs through the UNFCCC Online Registration System, with nomination deadlines that fall months before the conference and differ by category.