TBSG
Look at my post again. That may be what the definition is to you; however, it is at odds with the UK's doctrine that anything that flies is air power.
BH is force that is projected from a platform operating above the (albeit not very far above) the surface, as is airborne/space-based ISTAR, CAS, AOSE, OCA all of which have an effect on surface operations. However, they remain airpower. Just as NGS remain maritime power.
You are confusing the issue of what airpower is with componency. Moreover, the ownership of an organisation by a FLC (who are - in the main -deliverers of capability to the Jt Comd - so not vey front line at all) does not equate directly to componency. STC assets can and do operate in Land, Maritime, SF and Logs components. Similar can be said for FEs provided by FLEET and LAND. Air power can be, and is, delivered by elements of Maritime, Land, and Air components that are provided my FLEET, LAND, and STC. Air power does not equal RAF.
HQNI stopped 'owning' Heli-Tele with the formation of JHC (and with it JHF(NI)) albeit that they retained, iirc, OPCON.