We've a body that's oscillating in a fixed plane such that the torque on it is
$$\Gamma=-k \theta.$$
I went on an computed its energy ( kinetic + potential) and it was constant.
Why was it constant? It could only be constant if the force producing the torque was conservative but how can I see from the equation above that the force is conservative?
There are a few conceptual issues in your question.
I went on an computed its energy ( kinetic + potential) and it was constant. Why was it constant?
This way of putting it creates or betrays some conceptual confusion. The ability to compute the potential energy already presupposes knowledge that potential energy is well-defined for this situation. But knowing that the force admits a well defined notion of potential energy is identical to knowing that kinetic plus potential energy is constant. That's basically just the definition of potential energy, it's whatever function of position makes the total energy constant.
In other words, to put it briefly, having a formula for the potential energy presupposes that the total energy is constant.
It could only be constant if the force producing the torque was conservative
Not necessarily. It's theoretically possible that the force is really weird, for example depending not just on the position but also on time, but it sort of "conspires" to produce a nice torque.
but how can I see from the equation above that the force is conservative?
Because of the above, a more correct way of putting this question would be: how can I see that for this situation we can define a notion of potential energy such that the total energy is conserved? Which is equivalent to asking: how can I see that in this situation the kinetic energy only depends on the position (angle)?
The simplest way to see this I think is from the fact that the situation is mathematically analogous to the spring. Mathematically the situation looks identical to that of the spring if we replace the angular quantities (angle, torque, angular acceleration, moment of inertia) with the corresponding linear quantities (position, force, acceleration, mass). And we know that we can easily define a notion of potential energy for the spring, such that the total energy is constant, so we do exactly the same thing with the mathematically identical current situation.
This is Hooke’s law for a torsion spring, or the angular equivalent of Hooke’s law,
$$\tau = -k \theta$$
so it really makes more sense talking about the torque and not a linear force.
Upon inspection you can note that torque is directly proportional to the angular displacement and the potential energy stored in the spring is given by
$$U = - \frac{1}{2} k \theta^2$$
Since the original equation can be described as the derivative of the potential energy, you have by definition a conservative torque.
Is the force conservative which produced the torque?
Let's reason back the nature of force from energy rather than reason from forces to energy. We can write total energy in angular coordinate as:
$$ E = \frac{1}{2}I \dot{\theta}^2 + U(\theta) \tag{0}$$
Now in a hypothetical periodic motion where the oscillations don't die off in amplitude, this suggests that:
$$ \frac{dE}{dt} = 0 \tag{1}$$
Or,
$$ I \alpha \dot{\theta} + \frac{dU}{d \theta} \dot{\theta} = 0$$
Or,
$$ I \alpha + \frac{dU}{d \theta} = 0$$
Which is the conservative force equation.
Argument for (1) : Conservation of energy for an isolated system; if we had conservative forces at play $ \frac{dE}{dt}<0$
Remark on (0) : I assumed a potential purely dependent on $ \theta$ , you could do a potential which depends on both $r, \theta $ but that'd require the multi-variable chain rule.
A time dependent force implys no energy conservation. see here
