Geometric Interpretation of Matrix Additiom Is there a geometric meaning to matrix addition similar to how matrix multiplication acts as a linear transformation? I'm really curious thanks!

As you note, each matrix corresponds to a linear transformation. Given a matrix $A$, the linear transformation that $A$ corresponds to is defined via matrix-vector mulitplication.  In particular, if $A$ has size $m \times n$, then the corresponding transformation $T:\Bbb R^n \to \Bbb R^m$ is given by $T_A(x) = Ax$ for vectors $x \in \Bbb R^n$.
With that established, we can interpret the addition and multiplication of two matrices in terms of these linear transformations.  In particular: if $A,B$ are $m \times n$ matrices, then the transformation $T_{A + B}$ corresponding to the matrix $A + B$ is defined so that $T_{A + B}(x) = T_A(x) + T_B(x)$. That is, $T_{A+B} = T_A + T_B$. If $A$ is $p \times m$ and $B$ is $m \times n$, then the transformation $T_{AB}(x) = T_A(T_B(x))$. That is, $T_{AB} = T_A \circ T_B$.
Since we're focusing on addition, here is an example: take
$$
A = \pmatrix{1&0\\0&0}, \quad B = \pmatrix{0&0\\0&1}, \quad A+B = I = \pmatrix{1&0\\0&1}.
$$
Note that $I$ is a special matrix known as the "identity matrix".
The transformations corresponding to $A$ and $B$ are as follows:
$$
T_A(x) = \pmatrix{1&0\\0&0} \pmatrix{x_1\\x_2} = \pmatrix{x_1\\0}, \quad T_B(x) = \pmatrix{0&0\\0&1}\pmatrix{x_1\\x_2} = \pmatrix{0\\x_2}.
$$
In other words: $T_A$ is the projection onto the $x_1$-axis and $T_B$ is the projection onto the $x_2$-axis. Adding these two transformations together means that we get the output for $x$ by adding $T_A(x)$ and $T_B(x)$.  That is, we should have
$$
T_{A+B}(x) = T_A(x) + T_B(x) = \pmatrix{x_1\\0} + \pmatrix{0\\x_2} = \pmatrix{x_1\\x_2}.
$$ 
That is, adding $T_A$ and $T_B$ results in a transformation that produces the same input that we started with. This indeed matches up with the transformation corresponding to $A+B$. In particular,
$$
T_{A+B}(x) = (A+B)x = \pmatrix{1&0\\0&1}\pmatrix{x_1\\x_2} = \pmatrix{x_1\\x_2}.
$$
