How do hiring/promotion/grant committees assess individual applicants who've authored papers with huge teams
There's generally a way of assessing your contribution to the project even if it's enormous. So even if you're 29th author, if you were the senior manager of say particle detection and analysis, that's knowable. And they'll have a letter of recommendation from the project supervisor detailing your role.

And people on the committee (especially the person's department head) if they think you're great will advocate for you, the importance of your role, and the importance of your contribution to it.