So, does your partner ever talk to you about these comments? For example, do they feel the need to explain like, “I wrote this because…”? If they are completely silent, could it be that they are testing your reaction? I mean, do they prefer to go unnoticed rather than getting a reaction?
There’s also this: Let’s say their ex is seeing these comments, are there people in your mutual circle who are aware of this situation? In other words, is it just between the two of them, or are they trying to give off the impression to outsiders that “look, we’re still in touch” or “I’m still special to them”? I would consider this part too because there could be another dimension to this.
I think this is important too: Are those comments in a place where everyone can see them, or are those shares going to a shorter-term, limited audience like stories? Because what is done in front of everyone has a different meaning than what is done in a more “private” setting. Is it an attempt to draw general attention, or a desire to establish a hidden connection? One can derive a clue from this.
But if the ex is also silent in the comments, doesn’t that completely look like “an unreciprocated effort”? I mean, if they still want to be valued but there’s no reaction from the other side, it might be more about their own lack of self-confidence. Perhaps it’s an attempt to fill a void related to themselves, rather than the relationship.
I think the main issue here is how you learn these comments. Does your partner tell you directly, or do you find out and question? If there’s an attempt to hide something during the learning process or if there’s an indirect way of getting caught, this could be a sign questioning not only the honesty regarding the ex-partner but also the honesty towards you. This needs to be clarified.
So, does your partner consider whether the person they are commenting on is in a relationship? Is it just an action they see as “innocent from their perspective,” or are they taking into account the complications these comments might create in other people’s lives? Here, we can also question their point of empathy a bit.
What is the content of your ex’s posts? Is it an accomplishment, a special day, or something everyday? Are your partner’s comments appropriately polite for this content, or are they unnecessarily detailed participation? From this, the intention is somewhat understandable 
No one has focused on how you feel among so much analysis. Is there a situation that bothers you or not? If so, have you clearly defined its boundaries to your partner? Because before understanding what the other person is trying to do, what’s important is what you allow.
There’s also this: The timing of these comments is important. I mean, is it right after the ex’s post, or after a certain period of silence? If it’s a direct reaction, there could still be an active connection. But if some time has passed, it might be a more passive situation, like a “just came to mind” defense. The two are different things.
I think it’s important to consider not only how his ex-girlfriend reacted to these comments but also how much energy your partner dedicated to this “writing” process. Was it casual or did he put a lot of thought into what he wrote? Because one seems reflexive, while the other appears to be a search for a conscious connection.
I would ask directly. If instead of answering, they turn the topic to you, then there seems to be some trick there.
Is he considering what kind of impact his comments on his ex will have on his relationship with you? I mean, if he’s acting casually, taking into account that you might see this, then either he assumes you won’t make a big deal out of it or it’s not serious for him. Both situations could be testing your boundary perception.
Do you feel that there is still a private language between them, a tone only they can understand with this ex? Maybe it feels to you like a trace of such a bond, independent of the content of the comments. Is it just a comfort that doesn’t want to take risks, or is it the resurfacing of an old habit from the past?
And one more thing: Are these comments just written, or do emojis play a part too? Because sometimes a simple smiley face or “heart things” can open up another door of meaning. The tone of the message can be hidden in the details outside the text.
Are the posts they comment on public for everyone? If so, and they are aware of the possibility that you might see it, they might interpret not hiding it as a “clear conscience” sign. However, if it happens in a private setting, especially where you are unlikely to see it, I think the privacy aspect carries a more significant message.
You look at the content of the comments, but have you also focused on the tone? Is it sarcastic, serious, or is there an overly friendly subtext? Because just like the “writing process,” the atmosphere created by what is written is also important.
And there’s this: could commenting on your ex’s posts be a social power play? Like, a message saying, “I’m still here, just so you know.” Maybe it’s a challenge directed at you rather than to their ex 
But does he know that your trust in him has been shaken because of these comments? If you haven’t talked about this situation openly with him, he might not be aware at all. It would be difficult to expect change without showing that you feel uncomfortable.
Is your ex responding to comments? If there’s a dialogue going on there, the tone of the situation changes. Because there’s a difference between something done unilaterally and something done mutually 
This visible connection with your ex, how would it make you feel when you think of another ex or an old relationship? Maybe you need to turn inward to look at the situation from a different perspective. For instance, would it seem as normal if you were doing the same thing?