It was one his first philosophical writings; "Transcendence of ego".
The self does not, unlike pure consciousness disclose itself to immediate intuition. So it seems that according to Sartre the self belongs among the 'objects'* that transcend consciousness in the world.
In fact in this essay, he was attempting to cast off the ideas of Husserl while being influenced by them, a kind of crypto-idealism that contends that man is a spectator rather than being deeply committed to much of anything in the world, reflective of his later existential world view.
*An object is a philosophy term often used in contrast to the term subject. A subject is an observer and an object is a thing observed. (You likely know this already, only to clarify)
You sound knowledgeable about philosophy and philosophers. Great to learn this.
Why does it matter if the self is part of the things we observe in this world? As opposed to what? - aligned with a consciousness doing the observing? What would that affect? Or would it generate the detachment towards the world that you talk about when you refer to people being mere spectators?
Rather than viewing Sartre's point as an astute commentary on human nature, I can't help viewing it as telling us more about Sartre's psyche than about our own - that he was projecting his own detachment from the world onto others. There are people passionate about sports, the natural world (eg hiking in nature, gardening, photographing it) or collecting beautifully crafted material objects and appreciating them. There are people raising children, looking after elderly parents, working in homeless shelters, and saving cats and dogs like Eldad Hagar
An animal rescue hero: Eldad Hagar of Hope for Paws
I bet these people don't feel like mere spectators.
Sartre obviously lived much of his life in the mental, ideas realm - perhaps that got him down and, coupled with a huge egotism and self-centredness, he felt disaffected about life and accordingly injected his own bleak outlook into his philosophy. Perhaps if he's taken up some practical or more altruistic pursuits, his psyche would have been more balanced and he wouldn't have had such a big unconscious need to project it onto other people.
This echoes what I was saying above about denying any aspect of 'the human experience' at our peril. In astrological terms, it can be good to check whether we're paying homage to all four elements: water (the emotions), earth (the embodied and the practical), air (the mental) and fire (the motivation or willpower to get things done and assert ourselves). No one will ever be completely balanced in all these realms - that's what gives up personality, that we all have biases in different areas, and the ones with the biggest biases and blindposts often end up making history - whether as a terrorist or a contributor to philosophical thought.
Do you know anything about Sartre's biography and lifestyle? (Other than large-scale womanising!)