Normally (I'm my limited experience) things stay confidential because it is 'commercially sensitive' and could be detrimental to either or both parties. The length of someone's notice is a nonsense in this regard as it is literally impossible to keep confidential. If SG leaves after 4 months, everyone will know it is 4 months long, if he leaves after 6 everyone will know it is 6 etc. It will be apparent regardless, the only difference being that if was shared, it could help the club in the short term and would have zero detriment to Gardiner in any way that I could see. ETA- it's of course quite possible that SG is just being petulant and the club have to do things by the book as he would love for something to slip so he could take legal action. He absolutely seems that kind of person.
Perhaps I've worked in the lower paid public sector for so long that I take it for granted that things are open to scrutiny at all levels and your pay and contracts are public knowledge, you are accountable for every penny you spend etc.