It was distressing to see how much he'd aged these last few months since he'd battled with the decision to put the shop up for sale.
It means the same as "He hasn't eaten anything since this morning"?
Since has the same meaning in both your examples: since is a preposition here defining the timespan which runs from the prior event named by the object to the current Reference Time (RT), the time you are talking about.
In your first example, the prior event is his battle with the decision and RT is the past time at which he appeared old.
In your second example, the prior event is this morning and RT is the present, the time at which you are speaking.
Note that the use of since in your first example is correct only if the author means that the timespan in question, the last few months during which the subject has aged, started with the end of the battle over the decision, and the subject has aged since he lost the battle. We may guess that he lost the battle, and his distress at the sale of the shop is what has aged him.
But it is a very common error among both non-native and native users of English to employ a timespan as the object of since. If what the author means is that the timespan started with the beginning of the battle, and that the subject has aged during a battle that has gone on right up to the present, this use of since is incorrect. The author should say
It was distressing to see how much he'd aged these last few months during which he'd battled with the decision to put the shop up for sale.
OR
It was distressing to see how much he'd aged these last few months since he'd started to battle with the decision to put the shop up for sale.