Fix install script failing when piped in a shell

[begelundmuller]

This PR makes one fix and two improvements to the install script:

1. Fixes installation when the script is piped into sh
   • The bug was basename failing with an unknown flag error for the PARENT_NAME checks; this happened because the current shell process name has a dash prefix like -zsh when executing a pipeline
   • I fixed it by changing to a /dev/tty check instead of checking the parent process name
2. Moves the dependency checks to a single function such that all missing dependencies are printed before exiting
   • This ensures all missing dependencies are printed immediately, avoiding multiple rounds of install failures
3. Adds quotes around variables containing paths (was missing in some cases)

I have verified the script works with cat ./scripts/install.sh | sh in the following settings:

1. Local shell
2. Docker container
3. Claude shell
4. Claude tool call

Checklist:

• Covered by tests
• Ran it and it works as intended
• Reviewed the diff before requesting a review
• Checked for unhandled edge cases
• Linked the issues it closes
• Checked if the docs need to be updated. If so, create a separate Linear DOCS issue
• Intend to cherry-pick into the release branch
• I'm proud of this work!

[begelundmuller]

Note: Turned this into explicit calls to avoid relying on unquoted expansion

[begelundmuller]

Note: changed to explicit case handling instead of overriding args (which is fragile)

[begelundmuller]

Note: the pipe applied to true, but should apply to curl

[kaspersjo]

LGTM!