To kit someone or something out is to fully equip it, like you have gone all in and bought the lot. Can be clothes, gear, or a whole place. If you kit out a new office, it is not just a desk, it is the chairs, screens, plants, the fancy coffee bit, everything. Proper practical British phrase.
"They’ve kitted out the new gym with all the posh kit, even a smoothie bar. Dave’s like, I’m deffo starting Monday. Yeah alright mate, same as every January"