Based on historical evidence and total cover descriptions in the rules, the servant is unlikely to grant one-sided total cover. But ask your DM
There are magical effects that provide a near equivalent of one sided total cover, like Leomund's Tiny Hut (it's not exactly the same as you can not cast spells out of it).
Other spells do not describe the obvious, because the game expects you to apply common sense: if an object like a wall blocks line of effect, it grants cover to both sides. This can be asymmetrical for partial cover, but not logically for total cover which blocks all possible lines.
So the question is if the Servant has such a magical one-way force field that allows you to look out, or if it has physical windows, which would provide total cover to both outside and inside.
If we are allowed to take guidance from earlier editions, we can look at the description in 1e:
Mighty Servant of Leuk-O: Those who are most knowledgeable regarding ancient artifacts believe that this device is of the same manufacture as the Machine of Lum. The Mighty Servant of the famous General Leuk-O Is a towering automaton of crystal, unknown metals, and strange fibrous material.
Here the mention of crystal suggests that the way to look out are crystal segments. This is supported by the depiction of the sister item, the Machine of Lum the Mad: here the internal chamber is represented as a crystal compartment.
Another, similar item is the Apparatus of Kwalish. Here, it is explicitly stated that it has window panes on the front and sides (that can be shuttered).
The Siege Tower (DMG p 256) uses the same language. Historically such towers were also used to gain higher ground than the defending walks and clear them. The tower in the DMG instead is described as just a safe way to get up:
A siege tower is a mobile wooden structure with a beam frame and slats in its walls. Large wooden wheels or rollers allow the tower to be pushed or pulled by soldiers or beasts of burden. Medium or smaller creatures can use the siege tower to reach the top of walls up to 40 feet high. A creature in the tower has total cover from attacks outside the tower.
Lastly, the Ram, also under Siege Equipment contains this line:
Because of the gallery roof, these operators have total cover against attacks from above.
Nothing is mentioned about those outside the tower or above the ram also having total cover, as this is self-explanatory, at least for the ram. So there is precedent in the rules for describing two-way total cover by just stating one side has it.
One sided cover is sufficiently rare in the rules that one would be justified to expect something is explicitly stated about it. It often is difficult for the writers to spell out things that seem self-evident, so the absence of a clause regarding cover both ways may not necessarily mean there is one way-cover. I think, as far as one can sleuth about RAI, there isn‘t.
However, as you say, the description of the Servant in 5e does not really clarify how creatures can look out, and even the crystal might have magical properties to allow one-sided effects.
Therefore, your DM will have to decide how they rule this to work, like in many corner cases that do not have a clear-cut answer one way or the other.
That is also covered in Tasha‘s Cauldron of Everything, on page 4:
The rules of D&D cover many of the twists and turns that come up in play, but the possibilities are so vast that the rules can't cover everything. When you encounter something that the rules don't cover or if you're unsure how to interpret a rule, the DM decides how to proceed, aiming for a course that brings the most enjoyment to your whole group