«حَرْفُ الْبَاءِ لِلْإِلْصَاقِ فِي وَضْعِ اللُّغَةِ»
In its original linguistic function, ba denotes attachment: connecting one thing to another.
The connection is not limited to physical contact. In a contract it can connect an article of sale with its price; in a condition, the condition with its subject; or in a report, the statement with what it is about.
The central question is what is attached to what. Without answering it, one should not treat every ba as necessarily expressing a part, consideration or a redundant particle.