Problem 44263. Multivariate polynomials - emulate symbolic form

In Problem 44262 I asked you to create a class mPoly with overloaded multiplication, so a product of two polynomials can be expressed in the form p = p1*p2. However, the method of constructing these polynomials is still somewhat unintuitive. In the Symbolic Math Toolbox, one can simply define some variables,

syms x y z

and then create a polynomial:

p = 2*x*y + 3*x^5*z;

We would like to do something like that here. As a start, create a class mPolySym with properties exponents and coefficients, and varnames, where the first two properties are the same as in previous problems and varnames is a string array. The constructor should accept a numeric, char or string input, e.g.,

x = mPolySym('x')

x = 

mPolySym with properties:

        varnames: "x"
       exponents: 1
    coefficients: 1

r = mPolySym(pi)

r = 

mPolySym with properties:

        varnames: [0×0 string]
       exponents: 1
    coefficients: 3.1416

Also modify the method mtimes from the previous problem so it can multiply polynomials with different variable names.