Oauth token does not auto refresh when named credential is used

When a Salesforce Named Credential is used with a Salesforce SOAP API endpoint, the credential merge field {!$Credential.OAuthToken} does not automatically refresh the OAuth token when it expires. This is because Named Credentials rely on the external service returning HTTP 401 to trigger the token refresh flow. However, when a Salesforce SOAP API session is expired, the SOAP response returns HTTP 500 (not HTTP 401), so the automatic refresh is never triggered.
The following example demonstrates a callout using a Named Credential with the SOAP API. When the token is expired, the SOAP API response contains <sf:exceptionCode>INVALID_SESSION_ID</sf:exceptionCode> rather than HTTP 401, which prevents the Named Credential from auto-refreshing the token.

Example Callout (Apex):

The code sets the endpoint using the Named Credential callout prefix (callout:sfa/services/Soap/...), sets the Content-Type to text/xml; charset=utf-8, and embeds {!$Credential.OAuthToken} in the SOAP envelope's SessionHeader. When the token expires, the response is INVALID_SESSION_ID rather than a token refresh.

HttpRequest req = new HttpRequest();
req.setEndpoint('callout:sfa/services/Soap/u/37.0/00DA0000000Ah7w');
req.setMethod('POST');
req.setHeader('Content-Type','text/xml; charset=utf-8');
req.setHeader('SOAPAction','wewew');
String payload='<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:urn="urn:partner.soap.sforce.com">'+
   '<soapenv:Header>'+
         '<urn:SessionHeader>'+
         '<urn:sessionId>{!$Credential.OAuthToken}</urn:sessionId>'+
      '</urn:SessionHeader>'+
   '</soapenv:Header>'+
   '<soapenv:Body>'+
      '<urn:query>'+
         '<urn:queryString>select id from contact limit 10</urn:queryString>'+
      '</urn:query>'+
   '</soapenv:Body>'+
'</soapenv:Envelope>';
System.debug('');
req.setBody(payLoad);
Http http = new Http();
HTTPResponse res = http.send(req);
System.debug(res.getBody());