I'm from New Zealand, and this kind of stuff isn't a thing where I went (as far as I'm aware). Course enrolments open at some point (everything all at once), and you just log in and fill it out at some point over the multiple months between it opening and the due date for completing it. Some programs have limited admission (with their associated papers being restricted to those enrolled in that program), but limited space at the paper level (as opposed to the course level) and rushing to submit your paper selection just isn't a thing (as far as I'm aware).
1Password itself has native passkey support. I don't have experience with it on mobile, but on desktop browsers their extension overrides the build-in passkey support to use/store passkeys from/in 1Password (with a button to fall back to the built-in implementation for its storage, hardware tokens, QR code to use/store a passkey from/on a smartphone, etc).
Looks like on iOS it integrates with the native passkey support (so is usable anywhere native passkeys are supported). 1Password on Android looks to have similar integration, but only for apps at this stage (not websites, due to an Android limitation). So still a little while to go yet for "it just works" across all platforms.
My impressions with Typst have been very positive, though I did notice the same issue with Codly. Typst is still quite a new tool, so my expectation would be that this kind of issue will be fixed at some point.