What constitutes a matter being in the public interest with regards to the judiciary publishing a sentencing statement.

Sentencing in any given case including decisions relating to the publishing of sentencing statements is a matter for the court.
In general terms, a judge will often give reasons for imposing a particular sentence in court at the time of sentencing, or where the disposal is under challenge, in a subsequent report to the Appeal Court. The sentencing of convicted persons is usually announced orally. In certain cases a sentencing statement may also be published thereafter. The decision whether or not to publish a sentencing statement is at the discretion of the independent judge in the performance of their judicial function.