I got this to work using the following component. Any number of headers can be added as metrics tags by modifying the list getHeadersToTag statically

import static org.springframework.util.StringUtils.hasText;

import io.micrometer.common.KeyValue;
import io.micrometer.common.KeyValues;
import jakarta.servlet.http.HttpServletRequest;
import java.util.ArrayList;
import java.util.List;
import org.springframework.http.server.observation.DefaultServerRequestObservationConvention;
import org.springframework.http.server.observation.ServerRequestObservationContext;
import org.springframework.stereotype.Component;

/*
 * This component is responsible for extracting the headers(by default VCC-Client-Id) from incoming HTTP
 * request and appending it as tag to all the controller metrics.
 */
@Component
public class HeaderAsMetricTagAppender extends DefaultServerRequestObservationConvention {
  private static List<String> headersToTag;
  public static final String DEFAULT_VCC_CLIENT_ID = "default";

  static {
    headersToTag = new ArrayList<>();
    headersToTag.add(DEFAULT_VCC_CLIENT_ID);
  }

  @Override
  public KeyValues getLowCardinalityKeyValues(ServerRequestObservationContext context) {
    return super.getLowCardinalityKeyValues(context).and(additionalTags(context));
  }

  protected static KeyValues additionalTags(ServerRequestObservationContext context) {
    KeyValues keyValues = KeyValues.empty();

    for (String headerName : headersToTag) {
      String headerValue = "undefined";
      HttpServletRequest servletRequest = context.getCarrier();
      if (servletRequest != null && hasText(servletRequest.getHeader(headerName))) {
        headerValue = servletRequest.getHeader(headerName);
      }
      // header tag will be added in all the controller metrics
      keyValues = keyValues.and(KeyValue.of(headerName, headerValue));
    }

    return keyValues;
  }

  /**
   * The list of headers to be added as tags can be modified using this list.
   *
   * @return reference to the list of all the headers to be added as tags
   */
  public static List<String> getHeadersToTag() {
    return headersToTag;
  }
}

Don't add headers that can have large set value possibilities. This would the increase the metric cardinality\

Thanks to Bunty Raghani https://github.com/BootcampToProd/spring-boot-3-extended-server-request-observation-convention/tree/main