feat(chat-tab): update input and button focus styles, add auto-scroll and hide scrollbar

[vercel[bot]]

@eraykeskinmac is attempting to deploy a commit to the Upstash Team on Vercel.

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[ytkimirti]

Looks good to me, thanks a lot for the PR, the auto scroll was needed.

Can you run

pnpm prettier -w src

so the formatting would be correct too

[eraykeskinmac]

@ytkimirti its done can you check

[ytkimirti]

Perfect, thanks a lot ❤️