In `@packages/nuxt/src/pages/plugins/page-meta.ts`:
- Around line 253-285: The layout-object edge case must be handled when layout
has a props field but no name: inside the block handling prop.key.name ===
'layout' (and prop.value.type === 'ObjectExpression'), detect whether any
layoutProp with key.name === 'name' exists; if none, treat the entire layout
property as absent — remove/overwrite the layout property (respecting the same
nextProperty/comma removal logic used earlier) and still appendLeft layoutProps
as `layoutProps: ...` only if present; update the logic around
m.overwrite/m.appendLeft in the layout handling to first scan layoutProp keys,
conditionally remove the parent prop when name is missing, and keep existing
behavior when name exists.

In `@packages/nuxt/test/page-metadata.test.ts`:
- Around line 801-824: Rename the test description string in the it(...) block
from "should transform layout writen in object syntax" to "should transform
layout written in object syntax" and add two small tests alongside it: one SFC
where definePageMeta({ layout: { name: 'foo' } }) and assert the transformed
code yields layout: 'foo' with no layoutProps, and another SFC where
definePageMeta({ layout: { props: { bar: 'bar' } } }) and assert the transformer
(using parse/compileScript and transformPlugin.transform.handler) produces
layoutProps: { bar: 'bar' } and omits a layout string (or produces the expected
malformed-handling behavior), using the same pattern as the existing test to
locate code paths in transformPlugin.transform.handler and compileScript.

In `@packages/nuxt/src/pages/plugins/page-meta.ts`:
- Around line 268-293: The layout-object handling and the extractedKeys branch
can both call omitProp on the same prop causing double MagicString.overwrite;
modify the logic in the loop that processes props so that when prop.key.name ===
'layout' and prop.value.type === 'ObjectExpression' you perform the layout
extraction (appendLeft for name/props) and then skip the extractedKeys check
(e.g., add a continue or a conditional guard) to prevent calling omitProp twice;
reference the functions/identifiers isSerializable, extractedKeys, omitProp, and
the experimental extraPageMetaExtractionKeys option when locating the code to
change.