What is my error in reasoning about the complexity class $n^{o(1)}$
$n^{o(1)}$ converge to 1 (after all, $n^0=1$ )


You can't take the limit of one part without taking the limit of the other part, that doesn't give any useful information. If you take the limit of both parts, you get $\infty^0$, which is an indeterminate form.

It's easier to reason about exponentials with a constant base.
$$n^{o(1)} = e^{o(1) \cdot \ln(n)}$$
This way you can see that what matters is how fast the $o(1)$ function converges to $0$ relative to a logarithm.