[Python] Bypassing invisible reCaptcha with requests

I'm trying to make a scanner to a website using requests so the bot would be more efficient, and when I went over the Network Monitor to see the GET and POST request when emulating the process, I noticed that there's an invisible reCaptcha that prevents me to continue the process using the requests lib.

I tried simulating the exact GET and POST requests that I saw in the Network Monitor including doing it with the Session Object and saving the cookies I get, but the reCaptcha is what (I think) prevents me from actually keeping the interaction working. I tried looking for third party API, but what I understand it only works when you actually open the webdriver or you get a key to provide in the payload which in this case is not needed because the key is empty. Also I saw some solutions using selenium but I'm trying to avoid using it because it takes more time and I need to be as efficient as possible.

That's the code I tried to start the first steps:

import requests
from pypasser import reCaptchaV3

headers = {
'Accept' : 'text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,*/*;q=0.8',
'Accept-Encoding' : 'gzip, deflate, br',
'Accept-Language':'en-US,en;q=0.5',
'Connection':'keep-alive',
'Host':'agendamentosonline.mne.gov.pt',
'Sec-Fetch-Dest':'document',
'Sec-Fetch-Mode':'navigate',
'Sec-Fetch-Site':'none',
'Sec-Fetch-User':'?1',
'Upgrade-Insecure-Requests':'1',
'User-Agent':'what my broswer provides me'
}

session = requests.Session()
resp = session.get('https://agendamentosonline.mne.gov.pt/AgendamentosOnline/app/scheduleAppointmentForm.jsf',headers=headers)
cookies = requests.utils.cookiejar_from_dict(requests.utils.dict_from_cookiejar(session.cookies))
recaptcha_response_1 = reCaptchaV3('https://www.recaptcha.net/recaptcha/api2/anchor?ar=1&k=6LcKSTIfAAAAAEAxSrS8rAFiDux_eX2DBPnCXGkR&co=aHR0cHM6Ly9hZ2VuZGFtZW50b3NvbmxpbmUubW5lLmdvdi5wdDo0NDM.&hl=en&v=pn3ro1xnhf4yB8qmnrhh9iD2&size=invisible&cb=1ozwitjudoci')
recaptcha_response_2 = reCaptchaV3('https://www.recaptcha.net/recaptcha/api2/anchor?ar=1&k=6Ld7jDcgAAAAAJTt2PDioLNT69IwwEPvlhqa94K7&co=aHR0cHM6Ly9hZ2VuZGFtZW50b3NvbmxpbmUubW5lLmdvdi5wdDo0NDM.&hl=pt-PT&v=pn3ro1xnhf4yB8qmnrhh9iD2&size=normal&cb=ans33lqyh70u')
print(recaptcha_response_1) #
print(recaptcha_response_2) #

payload_1 = {
'javax.faces.partial.ajax': 'true',
'javax.faces.source': 'scheduleForm:tabViewId:dataNascimento',
'javax.faces.partial.execute': 'scheduleForm:tabViewId:dataNascimento',
'javax.faces.behavior.event': 'blur',
'javax.faces.partial.event': 'blur',
'scheduleForm': 'scheduleForm',
'javax.faces.ViewState': '-7004941669221712425:6117221410156700201',
'scheduleForm:tabViewId:ccnum': '****',
'scheduleForm:tabViewId:dataNascimento_input': '***',
'scheduleForm:tabViewId_activeIndex': '0',
'g-recaptcha-response': '',
'scheduleForm:respV2': ''
}

resp = session.post('https://agendamentosonline.mne.gov.pt/AgendamentosOnline/app/scheduleAppointmentForm.jsf',headers=headers,data=payload_1,cookies =cookies)

print(resp.text)


It does give me a response just a different response than the one I should get when it works

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