refactor: renames signer to auth session

[linnall]

Description

• renames packages signer, signer-web, signer-react-native, signer-web-example to auth, auth-web, auth-react-native and auth-web-example
• updates usage of signer to use the term "auth session" throughout v5 packages
• updates jsdocs code snippets to use term "auth session"

Pull Request Checklist

• Did you add new tests and confirm existing tests pass? (yarn test)
• Did you update relevant docs? (docs are found in the site folder, and guidelines for updating/adding docs can be found in the contribution guide)
• Do your commits follow the Conventional Commits standard?
• Does your PR title also follow the Conventional Commits standard?
• If you have a breaking change, is it correctly reflected in your commit message? (e.g. feat!: breaking change)
• Did you run lint (yarn lint:check) and fix any issues? (yarn lint:write)
• Did you follow the contribution guidelines?

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PR-Codex overview

This PR focuses on renaming and restructuring the @alchemy/signer package to @alchemy/auth, reflecting a shift from a signer-based approach to an authentication-centric model. It updates related imports, types, and configurations accordingly.

Detailed summary

• Renamed @alchemy/signer to @alchemy/auth.
• Updated imports across various files to reflect the new package name.
• Changed types from Signer to AuthSession in relevant functions.
• Adjusted configurations and package.json files for auth and auth-web.
• Modified documentation to align with the new authentication model.
• Updated example applications to use AuthSession instead of Signer.

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Project	Deployment	Preview	Comments	Updated (UTC)
aa-sdk-ui-demo	Ready	Preview	Comment	Sep 16, 2025 9:29pm

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[jakehobbs]

lgtm