Backport: feat(provider/anthropic): add support for new Claude Sonnet 4.6 model

[vercel-ai-sdk]

This is an automated backport of #12645 to the release-v5.0 branch. FYI @felixarntz
This backport has conflicts that need to be resolved manually.

git cherry-pick output

Auto-merging content/docs/02-foundations/02-providers-and-models.mdx
Auto-merging content/providers/01-ai-sdk-providers/05-anthropic.mdx
CONFLICT (content): Merge conflict in content/providers/01-ai-sdk-providers/05-anthropic.mdx
Auto-merging content/providers/01-ai-sdk-providers/index.mdx
Auto-merging examples/ai-core/src/generate-text/anthropic-reasoning.ts
Auto-merging examples/ai-core/src/stream-text/anthropic-context-management-clear-tool-uses.ts
Auto-merging examples/ai-core/src/stream-text/anthropic-reasoning.ts
CONFLICT (modify/delete): examples/ai-functions/src/generate-text/anthropic-context-management.ts deleted in HEAD and modified in 2a1c6642b (feat(provider/anthropic): add support for new Claude Sonnet 4.6 model (#12645)).  Version 2a1c6642b (feat(provider/anthropic): add support for new Claude Sonnet 4.6 model (#12645)) of examples/ai-functions/src/generate-text/anthropic-context-management.ts left in tree.
Auto-merging packages/anthropic/src/anthropic-messages-language-model.ts
Auto-merging packages/anthropic/src/anthropic-messages-options.ts
Auto-merging packages/gateway/src/gateway-language-model-settings.ts
error: could not apply 2a1c6642b... feat(provider/anthropic): add support for new Claude Sonnet 4.6 model (#12645)
hint: After resolving the conflicts, mark them with
hint: "git add/rm <pathspec>", then run
hint: "git cherry-pick --continue".
hint: You can instead skip this commit with "git cherry-pick --skip".
hint: To abort and get back to the state before "git cherry-pick",
hint: run "git cherry-pick --abort".
hint: Disable this message with "git config set advice.mergeConflict false"

[vercel]

Example file imports non-existent type AnthropicLanguageModelOptions from @ai-sdk/anthropic, causing a TypeScript compilation error.

[aayush-kapoor]

i don't think programmatic tool calling is available in v5.. might have to remove this docs section

[felixarntz]

Hmm, good point, hadn't considered that yet. I can see code_execution_20250825 in https://github.com/vercel/ai/blob/release-v5.0/packages/anthropic/src/anthropic-prepare-tools.ts#L73 - wouldn't that mean it is in v5, or does it require something else?

[felixarntz]

removed in 9012fb8