Also, Sam is afraid of grief, part 99 million.
Sam knows some. (And usually, not enough.)
He doesn't always notice emotional stuff on his own—not unless it’s a puzzle he can piece together from someone’s actions, or a situation he can map onto his own experience. His empathy is a pragmatic, lived-in, experience-driven thing.
He’s spent most of his life at the kids’ table, even when he was trying not to be, and his own needs and (in)stability are tragically often the center of a very small, very dry family desert with too little resources and few loved ones.
And like Dean sometimes wants Cas to be fine and invincible just so he doesn’t have to worry, Sam does too. In Sam's eyes, Cas is often the invincible, unkillable hero who always comes back no matter what. He gets up even when he fails. And even when he goes crazy, he pulls himself back together, (and quicker than Sam would've at that).
Even when Cas's dead, he doesn't die.
In 10x01, Cas is desperately holding his coughs in, and pulls away from the phone to cough, but when one of them slips through the receiver, Sam NOTICES:
SAM: The first lead, the first anything we've seen in... [Sam stops himself, hearing CASTIEL's nonstop coughing]
10x01
And yes, in this scene, Sam accidentally throws some passive-aggressive shade about his arm. He’s a friggin' whiner (he can't help it; he has terminal little brother syndrome), but overall, he changes his tune the second he hears Cas cough.
His eyes do the panicky back-and-forth tracky thing, and his excitement dies on the spot.
SAM: [after listening] Actually...you know what... now that I'm looking at this more I think I uh...I think I jumped the gun here, buddy. [...] I'm not, I'm not blaming anything on you. What happened, happened, and... you need to be worrying about yourself. I really shouldn't have bothered you.
10x01
But goshdarnit, if there’s something Sam usually isn’t, it’s thoughtful.
He could have invited Cas to the bunker—but the bunker, in Sam’s mind, is work, not a home. So giving Cas "time off" to "rest" and "worry about himself" feels like enough.
It’s a bit like how he and Dean treated Bobby sometimes. Cas is so dependable and self-sufficient in Sam's mind, that it doesn't occur to Sam to be caretaker in any form.
Sam’s got terminal kids-table-syndrome, with a three-course side dish of self-involvement, tunnel vision, and obliviousness. He is, in short, so emotionally stupid sometimes that it's almost-but-not-quite endearing.
(SEE Jody and Dean in 11x12: Dean undersells his own connection-making ability / empathy... and oversells Sam's.)
In 10x02, Sam calls Cas because, really, Cas is one of the only people he has left in his life. After all, they're short on family, short on friends. (And important to note, even the people they saved aren't around to ask for scraps—because Crowley killed off a whole slew of them in season 8, and Sam's still reeling from that.)
So Sam's turning to Cas, even when Cas is sick, like how he (and Dean) so often relied on Bobby, even when Bobby was actively suicidal / soul-crunched into his own demon deal / freshly getting used to his wheelchair.
SAM: Right. Now, Cas, listen. I know you're not feeling so hot, but this is kind of an “all hands on deck” situation here, so...
CASTIEL: So... I'll meet you there.
10x02
So, yeah. I seriously doubt Sam knows the full scope of how bad the grace situation is. Not saying he wouldn't rationalize it if he did, since he's a pragmatic guy. But fair's fair. He doesn't fully know here, and that's on PURPOSE. Cas wanted it that way:
HANNAH: I’m sorry. I just can’t see how Sam Winchester could ask you to drive all this way to help with his brother, knowing your condition.
[Castiel glances at Hannah, then turns back to the road.]
HANNAH: He doesn’t know … about how badly your borrowed grace is fading, does he?
CASTIEL: He knows some.
10x03
And there it is. Cas is being purposely cagey.
Yes, Sam is sometimes oblivious, but part of this whole dynamic is that Cas is notoriously super weird about showing WEAKNESS.
Anyway, I’d bet my Monopoly dog piece that Cas intentionally stayed away from the bunker in his downtime, trying to recover as much as possible in order to sure up enough energy to PRETEND to be strong.
Cas tells Hannah he wants to "say he's fine" so they can "avoid talking about something" no one can do anything about. He's given up on himself, because at this point it's looking very much like Dean died, and Cas will have to dispose of what's left of him.
BONUS SIDE NOTE: Cas also told Hannah he doesn't want help, from his family or anyone else, because the only way to help him is not one he wants to pursue. (Another reason he's keeping it to himself. He and Dean are THEMATICALLY united on that element this season.)
CASTIEL [lashing out]: And another angel should die so that I can be saved?! Is this really that hard to understand? Hannah...
10x01
Interestingly, though, Dean noticed Cas wasn't fine (re: batteries) back in season 9.
While it's true that Dean absolutely leaned into a sort-of endearing "Bobby-will-always-be-fine" dynamic, and perhaps clung to an invincible-Cas-hope early in their relationship, in the later years, it evolves.
Despite the occasional flash of hero worship (i.e. thinking Cas could time travel in s11), mostly Dean no longer believes that Cas will be fine...
...he just HOPES he will be.
(SIDE NOTE: In a hilarious full circle, Bobby ALSO expects a lot of Cas... Around and around we go!)
CAS: I'm fine, Dean.
DEAN: No, you're not. How long you got?
CAS: Long enough to destroy Metatron, I hope.
9x22
Anyway, it’s a massive difference with Sam, even in the terminal seasons. Sam has flashes of fear surrounding Cas’s death, but he really, really struggles to process it. (SEE: "I am spun out also.")
MOSTLY, he dissociates, throws himself into work, and refuses to face it.
(Kinda like how he rushes into the Eileen relationship in early s15 as a way to sidestep processing Mary, Jack, and Rowena.)
But unlike Dean, who grows into accepting and even fearing for Cas’s mortality, Sam seems to almost truly believe the line, "Cas will be fine. He always is."
(Cas HAS to be fine in order for DEAN to be fine, you see...)
I think the season 12 script cut line of Sam saying this
12x10 via @spnscripthunt-inactive
Because later, when Cas actually does die, Sam really doesn't believe his own eyes. He keeps asking Dean for confirmation. He looks, and he backs away, not believing, then bolts to address the next mission-oriented thing.
No-way, no-how running boy~~~~
BONUS: Sam & Jack ("Cas'll FIX things!!!")
SAM TO CAS (about dead Jack): Cas, is he here? C-C-Can you-- Can you...?
SEE also Sam vs grief with it comes to Dean-losing-Cas specifically.
Here's Sam realizing there's nothing he can do to ease Dean's grief about Cas, specifically, in the notorious Sam-freaks-out-and-is-bad-at-support 13x05... and 15x09 fake future, complete with with Sam’s beautiful jaw-wag of disbelief and panic-tracking eyes:
Look at him, the poor dude. He's TERRIFIED.
It's scary that Dean or Cas could die
Cas and Dean aren't just his family—they're his heroes He chafes at the thought of their mortality. It sends him into a tailspin every time.
CHUCK: No, this is more. This is...hope. Ah. That's what's stopping me – you. You still think that Dean and Cas are gonna fly through those doors just in the nick of time.
(SEE ALSO: Sam and deciding not to smash the orb)
He really does expect them to charge in and be unstoppable
Everything is gonna be fine... right?
JACK: You can't just give up!
SAM: What choice do we have?