Why is Public Key aggregation in MuSig described as a product of the public keys?
This is purely a matter of notation.
The points on the elliptic curve form a cyclic group. A group is a set with an associated identity element and a group operation. People need a symbol for that group operation. In some contexts it is more common to use an addition symbol (and multiplication representing repeated application of the group operation), and in other contexts it is more common to use a multiplication symbol (and exponentiation representing repeated application of the group operation).
Both notations are commonly used, and it has no effect on the actual operations. It's just a question of how to write what. There are even somewhat heated debates on this topic. You may even notice one of the MuSig2 paper's authors commenting in that thread.
One thing to point out that may explain this, is that the MuSig2 paper not ever mentions elliptic curves. It needs prime-ordered groups in which certain assumptions hold, but beyond that it could be any group - and the paper states, in Section 3.1, &quot;The group G is denoted multiplicatively&quot;. This is the case for most cryptography based on the discrete logarithm problem: it works for any group. And historically, the first type of groups used for this purpose were integers modulo a prime numbers (with certain other restrictions) - where multiplication is the obvious choice for the symbol. You may also notice it is called the &quot;discrete logarithm&quot; problem, and not the &quot;discrete division&quot; problem.
At the same time, in the context of elliptic curves, you're right of course that the operation is called point addition - and repeated application of it is called point multiplication. I personally prefer it as well, as means you get a more obvious correspondence between scalar and group operations (e.g. s = k + H(R,P,m)x for computing a Schnorr signature vs s·G = k·G + H(R,P,M)·x·G = R + H(R,P,m)·P for verifying it, as opposed to Gs = R·PH(R,P,m) in multiplicative notation), and avoids sometimes nested layers of superscripts in typesetting.
EDIT: Tim Ruffing pointed out to me that the real reason for using multiplicative notation in MuSig2 is because the paper started as a revision of the MuSig paper, which also used multiplicative notation. The MuSig-DN paper uses additive notation, however.