Selecting from XML in Snowflake

Question

I am trying to select the "Name" node of the XML file snipper from below but it is returning blank. Does anyone have any idea of why this is? Below is the xml code for the "author" node:

  <author>
  <time/>
  <assignedEntity>
     <representedOrganization>
        <id extension="194123980" root="1.3.6.1.4.1.519.1"/>
        <name>Physicians Total Care, Inc.</name>
        <assignedEntity>
           <assignedOrganization>
              <assignedEntity>
                 <assignedOrganization>
                    <id extension="194123980" root="1.3.6.1.4.1.519.1"/>
                    <name>Physicians Total Care, Inc.</name>
                 </assignedOrganization>
                 <performance>
                    <actDefinition>
                       <code code="C73607" codeSystem="2.16.840.1.113883.3.26.1.1" displayName="relabel"/>
                    </actDefinition>
                 </performance>
              </assignedEntity>
           </assignedOrganization>
        </assignedEntity>
     </representedOrganization>
  </assignedEntity>

and here is the Snowflake code I am using:

 SELECT 
  XMLGET(name.value, 'name'):"$"::string  name
FROM 
  dailymed_xml,
  LATERAL FLATTEN(GET(src_xml, '$')) author,
  LATERAL FLATTEN(GET(author.value, '$')) time,
  LATERAL FLATTEN(GET(time.value, '$')) assignedEntity,
  LATERAL FLATTEN(GET(assignedEntity.value, '$')) representedOrganization,
  LATERAL FLATTEN(GET(representedOrganization.value, '$')) id,
  LATERAL FLATTEN(GET(id.value, '$')) name
  
WHERE 
  GET(author.value, '@') = 'author' AND 
  GET(time.value, '@') = 'time' AND
  GET(assignedEntity.value, '@') = 'assignedEntity' AND 
  GET(representedOrganization.value, '@') = 'representedOrganization' AND 
  GET(id.value, '@') = 'id' AND 
  GET(name.value, '@') = 'name';