ci: many examples fixes

[anthonyshew]

Description

After working well for a brief moment in time, the examples are inexplicably quite broken somehow. This PR has a good number of fixes to try to unstuck them once again:

• I had to install ESLint into each package to fix pnpm usage. Unfortunately, this isn't in service of making the examples better. Rather, we were getting the ESLint version running from the outer repository when there wasn't an ESLint specified in the repo.
• This PR improves logging with a tee for CI debugging. We previously had poor visibility in CI and were getting vastly different behavior between CI and local (still are 😞). The tee should help a little.
• We're using a real temp_dir now. This was done to try to fix the aforementioned ESLint issue, but it's probably what we should have been doing anyway before.
• We were accidentally running the kitchen-sink tests twice and never running basic due to a copy-pasting error. My bad.

Testing Instructions

CI

[vercel]

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Name	Status	Preview	Comments	Updated (UTC)
examples-basic-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-designsystem-docs	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-gatsby-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-kitchensink-blog	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-native-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-nonmonorepo	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-svelte-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-tailwind-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am
examples-vite-web	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 11:04am