will this be decidable or partially decidable? $A=\{\langle M \rangle \mid M \text{ is a turing machine and }|L(M)|\geq3\}$

Since Recursive enumerable languages are turing enumerable, so listing of all strings of the language in finite time is possible. Then deciding whether cardinality is greater than 3 should be decidable. But the material that i have been studying says it is partially decidable. Which one is right?
The language is clearly not decidable; use Rice's theorem. See e.g. our reference question.

We can certainly simulate $M$ on every input by dovetailing and count accepted inputs; if $|L(M)| \geq 3$ our counter hits three after finite time and we accept, otherwise we loop. Therefore, $A$ is semi-decidable.