There is no example for the extension. Component was added to the resource in summer 2022. Sushi has no problem with the syntax. Don't know if the issue is the extension or if the element component has not been added somewhere.

In profile on ManufacturedItemDefinition:

• component 1..* MS
• component ^type.profile = http://hl7.org/fhir/us/pq-cmc/StructureDefinition/pqcmc-product-part
• component ^type.profile.extension.url = http://hl7.org/fhir/StructureDefinition/elementdefinition-profile-element
• component ^type.profile.extension.valueString = "ManufacturedItemDefinition.component"

generates these errors:
Stack Dump (for debugging): (02:53.825)
java.lang.Exception: Error generating snapshot for C:\FHIR-us-pq-cmc\fsh-generated\resources\StructureDefinition-pqcmc-product-part(pqcmc-product-part): Unable to generate snapshot for http://hl7.org/fhir/us/pq-cmc/StructureDefinition/pqcmc-product-part in C:\FHIR-us-pq-cmc\fsh-generated\resources\StructureDefinition-pqcmc-product-part
at org.hl7.fhir.igtools.publisher.Publisher.generateSnapshots(Publisher.java:5803)
at org.hl7.fhir.igtools.publisher.Publisher.loadConformance(Publisher.java:4959)
at org.hl7.fhir.igtools.publisher.Publisher.createIg(Publisher.java:1085)
at org.hl7.fhir.igtools.publisher.Publisher.execute(Publisher.java:914)
at org.hl7.fhir.igtools.publisher.Publisher.main(Publisher.java:10727)
Caused by: org.hl7.fhir.exceptions.FHIRException: Unable to generate snapshot for http://hl7.org/fhir/us/pq-cmc/StructureDefinition/pqcmc-product-part in C:\FHIR-us-pq-cmc\fsh-generated\resources\StructureDefinition-pqcmc-product-part
at org.hl7.fhir.igtools.publisher.Publisher.generateSnapshot(Publisher.java:5875)
at org.hl7.fhir.igtools.publisher.Publisher.generateSnapshots(Publisher.java:5801)
... 4 more
Caused by: org.hl7.fhir.exceptions.DefinitionException: Unable to find element ManufacturedItemDefinition.component in http://hl7.org/fhir/us/pq-cmc/StructureDefinition/pqcmc-product-part
at org.hl7.fhir.r5.conformance.ProfileUtilities.processPaths(ProfileUtilities.java:1341)
at org.hl7.fhir.r5.conformance.ProfileUtilities.generateSnapshot(ProfileUtilities.java:724)
at org.hl7.fhir.igtools.publisher.Publisher.generateSnapshot(Publisher.java:5870)
... 5 more