doc: split install commands for copy

[yanCode]

Description

Checklist

• [ *] I have run pnpm stylecheck and pnpm typecheck
• [ *] I have run pnpm test and all tests pass
• I have added tests for my changes (if applicable)
• [ *] I have updated documentation (if applicable)

Changeset

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What I did:

Split the install commands into separate code blocks so copy works per package manager in README.md for both v5 and v4 sections.

Without this fix, if a user clicks the copy icon in the install command section, all commands of all package managers will be incorrectly copied.

[robert-j-y]

@yanCode when you get the chance, can you make this adjustment for our new v2 release? Which is based on the AI SDK v6, and not v5 anymore. The README in this PR is outdated currently.