I don't think you should tell about the job, presuming that you heard about it in confidence.
It is superficially attractive for authority to have a network of informers in place, and for nobody to be able to speak to anybody else in confidence where such confidence keeps information from the authority. So, one might think that one's duty to one's employer is to run straight to your boss's boss with the news. However, in practice this degrades what I'll call for want of a better word "society". Where there is no outright wrong-doing it's better in general, in the long run, for colleagues to be able to speak to each other in confidence, and by no means is it outright wrong-doing for an employee to seek and secure a new job. Betraying a confidence trades this general benefit of trust among colleagues, for a specific benefit of dealing with your boss's current BS.
One result of this is that "snitches get stitches", sometimes even from the authority that they inform to, never mind their peers. It may not be right or fair, but you have to take into account that it probably won't be taken as you having done anyone a favour. If your boss was stealing from the warehouse then betraying the confidence would be not only approved of but demanded by the senior management (and the law). That would be outright wrong-doing.
Despite this I do think you're entitled to call out the "F--- it attitude" and the fact that you're now doing a lot of his work, but do so in the way that you would do if you didn't know the reason behind it. It's not your job to report to the company as a whole on your boss's motivations, but it is your job to report what work you're doing.
Frankly, if you're in the running to get the job, then simply mentioning that you're already doing much of the work, without making a complaint of it, probably does you no harm. So you might choose not to complain anyway, if it's to your benefit not to. Try to get enough written down, that when you're considered for the post you can say, "I already have proven experience of doing X, Y and Z required in this role". But if the workload of the two jobs combined is unmanageable, or if your boss's attitude is harming things that you can't just cover, then you're definitely entitled IMO to address the fact that your boss is severely underperforming. You don't have to provide the reason your boss has chosen to severely underperform.
If this calls unwelcome attention on your boss, with the result that they somehow figure out that he's planning to leave, well, maybe he should have carried on doing his job up to the point he actually did leave. So another thing you can try is to say, in whatever words are appropriate to your relationship with your boss, "you wouldn't take this view if you weren't about to leave, and people are going to notice the sudden change. If you don't care about them finding out then would you mind just giving them the date so that we can all work towards a clean handover?".