Backport: fix(docs): update reasoning property names to match API 5.0

[vercel-ai-sdk]

This is an automated backport of #10966 to the release-v5.0 branch. FYI @AryanBagade
This backport has conflicts that need to be resolved manually.

git cherry-pick output

Auto-merging content/docs/07-reference/01-ai-sdk-core/01-generate-text.mdx
CONFLICT (content): Merge conflict in content/docs/07-reference/01-ai-sdk-core/01-generate-text.mdx
Auto-merging content/docs/07-reference/01-ai-sdk-core/02-stream-text.mdx
Auto-merging content/providers/01-ai-sdk-providers/05-anthropic.mdx
Auto-merging content/providers/01-ai-sdk-providers/08-amazon-bedrock.mdx
Auto-merging content/providers/01-ai-sdk-providers/16-google-vertex.mdx
error: could not apply e5a42f715... fix(docs): update reasoning property names to match API 5.0 (#10966)
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"