The Carthaginian senate made decisions from Carthage, they sent armies to Spain, to Sardinia, Sicily and to Italy from Carthage. Of course, they raised armies in Spain too (two of which made it to Italy from the land route), some of which were shipped to Africa in preparation for naval invasions. The decision in 216 BC to have Hasdrubal march to reinforce his brother was decided in Carthage, not Spain (in fact, he was fairly surprised by the decision, and urged the senate to reinforce Spain if he were to leave, which they did, twice, once before he left, and once after his heavy defeat at the Battle of Dertossa in 216/early 215 BC against the Scipio brothers!)
I never meant the second was a war upon the seas, (there were precious few naval battles during the war as you rightly pointed out -though Lilybaeum was not the only one - there was a couple in Spain, one of which is recorded in the only fragment we have of Hannibal’s biographer Sosylus) and of course, there was plenty of coastal raiding from both Roman and Carthaginian fleets, but essentially, much deployment came from Carthage during the war, across the sea after Hannibal’s initial invasion from Spain.
It is entirely disingenuous to ignore the importance of the med during the war, and the fact that most strategic decisions for the war were made in Carthage (generals largely had control over their own theaters, such as Hasdrubal in Spain, and Hannibal in Italy, but overall, the important strategic decisions were made by the senate at Carthage, which they adhered to). As I said, there was a land route, obviously connected from Iberia to Italy, but the sea still played a major part in the contribution of the war (dictating much of Hannibal’s strategic policies in capturing ports in southern Italy), and that there was separation from part of its Empire, coincidentally, its head (the senate) separated by the Med. � �
Hannibal’s campaigns were conducted across the land route, where he actually received more supplies and manpower on the Italian peninsular than Spain for the majority of the war, but looking at the Carthaginian war effort as a whole, I can understand the ‘separated by the sea’.