Here is a list of all the politics and social commentary Andy Weir did in fact include in the Project Hail Mary book that I can recall at the top of my head:
When Grace is still incredibly amnesiac and manages to remember what his apartment looks like, he remarks the lack of feminine touches in the decoration and casually wonders if this means he is single or maybe gay.
Upon learning of the astrophage problem, all the nations of the world get their shit together in record time and give Stratt basically unlimited power, authority and resources to do whatever is necessary to save Earth. This itself is a political choice. Pair it with the vastly different real world response world leaders have to climate change and it becomes a social commentary, sorry Andy but it really does.
The reason Grace decides to join the Hail Mary project is because of his students. He's in the middle of a class when he realizes the incredibly hard and bleak future that awaits his students due to the cooling Sun, and tells Stratt he wants to keep helping.
Shortly after figuring out how astrophage reproduce on his own, Grace is taken to the aircraft carrier, where he meets for the first time the other scientists involved in the project. After explaining his findings, a Chinese scientist announces their team has been able to reproduce Grace's findings, the implied reason being they had somehow spied on them.
During one of his first conversations with Rocky, Grace remarks on an unexpected hurdle of meeting aliens: pronouns. His conclusion is to just shrug and slap he/him pronouns on Rocky. There are no further conversations about this topic, not even when both of them are able to communicate fluently. Grace doesn't re-examinate his pronoun choice any further, nor, despite having a PhD in molecular biology and being curious about things like how Eridians eat, ask about Eridians' concepts of sex and gender.
Following that previous point, when Rocky mentions having a mate back home, Grace chooses for said mate the name Adrian. This is yet another reference to the Rocky movies, albeit a more obscure one, and a lot of the people that didn't realize this simply read both Rocky and Adrian as male and therefore gay.
One last bit re gender and sexuality is the fact that at no point during the book does Ryland Grace, a single man of unspecified sexuality, lament being single or express any sexual desires, which is why many people read him as being on the asexual spectrum.
The movie had to gloss over many things and completely skip over others, some of these later things were the incredible sacrifices and hardships Earth had to go through to survive until hopefully Project Hail Mary managed to find a solution to the astrophage problem. First off, in order to produce the astrophage fuel for the ship they paved a huge chunk of the Sahara desert, which had devastating ecological and climate consequences, altered or destroyed the homes and livelihoods of millions of people and created tons of refugees. Also, in order to win time and counter the effects of the cooling Sun, they start to nuke chunks of fucking Antarctica, because making climate change worse will make Earth hotter and therefore buy them time. The first time the scientist (a self-declared hippie ecologist) in charge of this orders the release of the bombs, he understandably breaks down and starts to cry. Needless to say, nuking the fucking Antarctica raises sea levels and also has horrendous ecological and climatic consequences and once again would in fact create millions of refugees. The fact that the book doesn't dwell on the consequences of any of these two actions doesn't change the fact that we as readers are supposed to extrapolate and put two plus two together whether Andy intended to or not. Expecting otherwise is frankly insulting.
At one point Stratt tells Grace what will happen to Earth while they await for the solution to the astrophage problem. She talks about the famines and how many people will die, but that's just the people that will starve to death. Millions more will die in the wars that will break out all over the planet because there is no way the richer and more powerful nations will be willing to share resources equally with the rest.
Grace gifts Rocky, a member of an alien species, a laptop that contains the sum of all human knowledge, history and media. He knows Rocky, but has never met other Eridians, and despite this he chooses to give it to them.
The fucking foundational plot of the book is interspecies collaboration, trust, and friendship. Choosing to meet and befriend an alien despite all the possible risks and dangers is just as political of a choice as choosing to kill an alien would be.
Andy Weir is very good at writing Cosmic Hope books about Space MacGyvers, but writing any kind of story is inherently full of a myriad of political and social commentary choices, whether you want to or not, and whether you realize it or not. Being unable to see or willing to admit this makes him a worse writer and frankly greatly mars part of his supposed genius.