Hi!! I'm a big fan of how you write Jin and I love strega a lot and I've had this wondering to myself about how Jin must have felt when Chidori was in hospital and whether she ever wanted to visit her (even though it would've been pretty difficult to do). I think the situation would've brought up a lot of bad memories for Jin and Takaya and I'm not sure how they'd feel about it so I thought I'd ask your opinion! (Btw I'm referring to in canon rather than Standing in Her Own Shadow since I can imagine that might play out differently, if at all)
So! As much as I wish Reload had done more with it (and god do I hate a lot of the extra Strega content for missing the point) we do get a scene on 9/7 for them discussing rescuing Chidori, which Takaya shoots down, saying it'd be what they expect and to wait for an opening. Jin basically treats Takaya's words as gospel, so until Takaya decides when and where, I think any feelings of wanting to see Chidori get pressed down. Jin immediately concedes the argument and even apologises for losing their cool.
I still think Jin's persona, Moros, has some latent navi ability (for Strega to somehow always be on the scene first even after Chidori vanishes) but attuned to Shadows (I did a thread about it over on my twitter, maybe I should post it here) than people, so any research on where Chidori was probably came from brute-forcing a check.
The stageplay has Jin drag Takaya to see Chidori after the Moonlight Bridge fight, but we don't get much context as to *why* they don't take her out then, so as much as I enjoy P3WM, I'll discount that from this argument.
What seems to be the 'deciding factor' that isn't fully communicated is the fact SEES (sans Ken) are in Kyoto until the 20th and the Kirijo group are in utter chaos after Takeharu dies (covered even more in the NewMoon/FullMoon Drama CDs) which combined with the knowledge of Jin's hacking abilities means Strega probably timed it (the late 21st/early 22nd move in November) perfectly. It's still a weird scene overall though. Jin bombing a hospital is reported on the news, yet Mitsuru and Akihiko don't immediately think to check her ward before Fuuka does that night's operation. Very weird bit of Strega making noise and nobody reacting, honestly.
Either way, we again see in Weird Masquerade how Jin instinctively goes to stand by Chidori's side and reassure her, so I think there's a lot of resentment at themselves and Takaya for taking around 3 months to come grab her. Jin hates the Kirijo group and what happened to them, and god knows what Kirijo are doing to Chidori, yet she's being ordered to not act. It's no wonder that Jin spirals so hard (made abundantly clear in P3WM) after Chidori dies. They break out one of the people they're closest to (if not the closest, considering their weird but sweet dynamic in P3SC) and argue, then die. If your last memory of someone is 'waiting, arguing and dying' you're going to constantly replay that in your head.
So overall, Jin would've gone to see Chidori, but their deference towards Takaya means they suppressed their true feelings on the matter until it was too late. Sorry if that was a little rambly, hope it helps
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Material referenced:
Persona 3 Reload
Persona 3 FES
Persona 3 Portable
Persona 3 The Weird Masquerade
Persona 3 Shadow Cry