The Noble Truths are conditioned because they require the experienced world to be empty of Essence (the Truths would not hold in a world where an independent Self was perceived and directly knowable in the here and now). The path is conditioned as it is an Eightfold Path, requiring right view, right though etc. Nibbana is unconditioned, but when brought within the confines of thought or language it will be conceived as conditioned, because language and thought are conditioned experiences.
A subject's direct knowledge of the cessation of the 'sphere of neither perception nor non-perception', and that there is no thing further beyond that, does not fit into language very well if you wish to use the verb 'to perceive' with regards to what the subject is experiencing! Because this is the point at which all mental fermentations cease (whether perception or non-perception), the mental state is beyond designation, if being reasonable. I would say it is fair to say that it is unconditioned in the here and now of that individual. The process of arrival to it however, must be conditioned on previous meditative states. And because the mind that experiences direct knowledge is still conditioned by the body, there will be an exit from the perception of cessation. So yes, the experience of Nibbana is impermanent (as any and all experiences must be), the knowledge of it however can carry through beyond the experience, and remain 'permanently' with the Arahant until their parinibbana. (That's my thought, but I am still thinking it through to be honest!)
In Majjhima Nikaya 1 it is stressed that conceiving of any thing beyond the direct knowledge of that thing (going beyond impermanence, suffering and non-Self, or not 'treating this as this and that as that' in short) is effectively wrong view. The direct knowledge of Nibbana must therefore be unconditioned, because only conceptual construction brings it down into the forum of the conditioned, and otherwise its 'being' and its 'perception' would not equate, which would be delusion for the subject of the perception.
https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth is a very interesting article on the logic within the catuskoti that may provide some clearer information too!