RestTemplate not passing bearer token correctly

Question

I need to remove WebFlux dependencies from one of our repos. When I switch from WebClient to RestTemplate, I get 403 errors, invalid authorization.

The original code:

        return webClient.post()
                .uri(String.join("/", jobConfig.getBaseUrl(), JOB_RUN_NOW_PATH))
                .header(HttpHeaders.AUTHORIZATION, jobConfig.getAccessToken())
                .header(HttpHeaders.CONTENT_TYPE, MediaType.APPLICATION_JSON_VALUE)
                .body(BodyInserters.fromValue(jobBody))
                .exchangeToMono(this::handleResponse);

...

    private Mono<JobResponseBody> handleResponse(ClientResponse clientResponse) {
        return clientResponse.bodyToMono(JobResponseBody.class);
    }

webClient instantiation:

    @Bean
    public WebClient webClient(WebClient.Builder builder) {
        return builder.build();
    }

The new code:

        HttpHeaders headers = new HttpHeaders();
        headers.setContentType(MediaType.APPLICATION_JSON);
        headers.add(HttpHeaders.AUTHORIZATION, jobConfig.getAccessToken());
        HttpEntity<JobRequestBody> request = new HttpEntity<>(jobBody, headers);
        return restTemplate.exchange(
                String.join("/", jobConfig.getBaseUrl(), JOB_RUN_NOW_PATH),
                HttpMethod.POST,
                request,
                JobResponseBody.class
        ).getBody();

restTemplate instantiation:

    @Bean
    public RestTemplate restTemplate() {
        return new RestTemplateBuilder().build();
    }

When I run the WebClient code, I receive a successful response. When I run the RestTemplate code, I receive a 403 Invalid access token error. I have verified that the token in both cases is in the correct form. I am using Spring Boot 2.6.7. The authorization tokens are in the format "Bearer dapic..." as confirmed by inspection in debugging mode. The url is also the same. I am calling an actual external service in the integration test.

How do I successfully pass authorization in RestTemplate?