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The way you define h makes it a Python function, so that, when you call h at the floating-point number 4.3, it is evalued by entering twice the while loop and then taking the absolute value of 4.3-2-2, that is 0.3.

However, when you call h at the symbolic expression x, the while loop is not entered since:

sage: bool(x>1)
False

hence, the abs function is called at the symbol x and what is returned is the abs(x) symbolic expression, see:

sage: abs
<built-in function abs>
sage: type(abs)
<class 'builtin_function_or_method'>

sage: abs(x)
abs(x)
sage: type(abs(x))
<class 'sage.symbolic.expression.Expression'>

Hence plot(h(x),x,0,5) is the same as plot(abs(x),x,0,5). The syntax plot(foo,x,0,5) is for plotting symbolic function, which is OK since abs(x) is a symbolic function, but it is not what you expected. If you want the plot function to evaluate the function foo at various floating-points between a and b to make the graphics, the syntax is just plot(foo,a,b), without mentionning any symbol.

Hence, you should simply call

sage: plot(h,0,5)