How to login then scrape multiple pages using Scrapy

Question

My task is to visit a starting page in order to get some cookies, then login and finally navigate to a page/pages. My code below:

class ExampleSpider(scrapy.Spider):
    name = "test"

    HEADERS = {
        'user-agent':   'My User Agent',
        'accept':   '*/*',
        'accept-encoding':  'gzip, deflate, br'
    }

    AUTH_REQUEST_HEADERS = {
        'accept':   '*/*',
        'x-li-lang':    'en-US',
        'accept-encoding':  'gzip, deflate, br',
        'token':    'default token',
    }

    
    def start_requests(self):
        return [
            Request(
            "https://www.example.com",
            headers = self.HEADERS,
            ),]

    def parse(self, response):
        cookies = response.headers.to_unicode_dict()['Set-Cookie']
        session_pattern = re.compile('JSESSIONID="(.+?)"')  
        JSESSIONID = session_pattern.findall(cookies)[0]
        return FormRequest(
            "https://www.example.com/authenticate",
            formdata = {
            "session_key": '[email protected]',
            "session_password": 'password',
            "JSESSIONID": JSESSIONID
        },
            headers = self.AUTH_REQUEST_HEADERS,
            callback=self.fetch
            ),
            
            

    def fetch(self, response):
        yield Request("https://www.example.com/api/user1",callback=self.processor)

    def processor(self,response):
        ...

The first request and the authentication need specific headers hence why I used return. However the last call for fetch returns a 403 error. The login step in parse is successful so not sure why my last step is not authenticated. How can I ensure the calls under fetch are also using the authenticated session? I'm still starting out with scrapy so also happy with any tips to improve my code