Here another solution using the API:

import requests

def get_all_results():
    headers = {
        'hostname': 'http://mst.local:3001'
    }

    payload = {
        'key': 'a2369450-5ec7-494c-b910-d72074a73af9',
        'documentTypes': ['articlePage'],
        'subjects': [],
        'categories': [{'name': 'Publikation'}],
        'takeAmount': 100,
        'skipAmount': 0,
        'direction': 'descending',
        'UserTextInputField': ''
    }

    url = 'https://search.mst.dk/api/News/Search'
    
    results = []
    while True:
        response = requests.post(url, headers=headers, json=payload)
        data = response.json()
        results.extend(data['searchResults'])
        payload['skipAmount'] += payload['takeAmount']

        if len(results) >= data['pagination']['totalResults']:
            break

    return results


results = get_all_results()

print(f'{len(results) = }')

*This takes about 30-40 seconds to fetch all 3201 results, you can use async for faster time.

next_button = driver.find_element(By.XPATH, "//li[contains(@class, 'Pagination_Pagination_next')]/a[@rel='next']")

Although the XPath expression in your above code is correct, for some reason it is not clicking the element. I used ActionChains as below and it successfully clicked the next button.

next_button = wait.until(EC.element_to_be_clickable((By.XPATH, "//a[@aria-label='Next page']")))
actions = ActionChains(driver)
actions.move_to_element(next_button).click().perform()

Here is a full working code which will scrape the pages in a loop.

Note: I am scraping the first 3 pages and scraping the search results headings you can scrape whatever you want:

from selenium.webdriver import ActionChains
from selenium import webdriver
from selenium.webdriver.support.wait import WebDriverWait
from selenium.webdriver.support import expected_conditions as EC
from selenium.webdriver.common.by import By

def click_next_page():
    next_button = wait.until(EC.element_to_be_clickable((By.XPATH, "//a[@aria-label='Next page']")))
    actions = ActionChains(driver)
    actions.move_to_element(next_button).click().perform()

def extract_headings(wait):
    headings = wait.until(EC.visibility_of_all_elements_located((By.XPATH, "//li//h3")))
    search_results_headings = ""
    for heading in headings:
        search_results_headings += "n" + heading.text
    return search_results_headings

driver = webdriver.Chrome()
driver.get("https://mst.dk/publikationer")
driver.maximize_window()
wait = WebDriverWait(driver, 10)

# Use below line of code only if you see accept/reject cookies pop-up
accept_all = wait.until(EC.element_to_be_clickable((By.ID, "CybotCookiebotDialogBodyLevelButtonLevelOptinAllowAll")))
driver.execute_script("arguments[0].click();", accept_all)

search_results_headings = ""
# Below for loop iterates 3 times, so 3 pages will be scraped, if you want more pages change the range accordingly
for _ in range(3):
    search_results_headings += extract_headings(wait)
    click_next_page()

print(search_results_headings)

Console output:

Diffus forurening med PFAS i jord, grundvand og overfladevand
Digitale værktøjer til klimatilpasning
Performancebenchmarking
Oprensning af PFAS-forurening i jord, slam og vand - Test af teknologier i praksis
Lokalt funderede analyse – afrapportering
Maritime Emissionsløsninger i Kystnære Farvande
Biokinetisk lattergasreduktion i renseanlæg
Inter DAN NRW
Gennemførelse og anvendelse af slamdirektivet 2023
CombiControl - Combining above- and belowground biological control agents for improved pest control in strawberry tunnel production
Affaldsstatistik 2022
Scientific investigation of ballast water discharge - Random checks on ships in autumn – winter 2022
Control of Biocides 2023
Ny kosteffektiv teknologi til måling af klimagasudledninger fra renseanlæg
Recycling potential of separately collected post-consumer textile waste
Modelling and mapping ­pesticide exposure risk at the catchment scale (MOMAPEST)
Indberetning af status for anvendelse af almene vandforsyningsboringer i Virk.dk
PFAS i jord - International screening af andre landes praksis for håndtering af jord med PFAS
Anbefalinger til screening og kortlægning af bygge- og anlægsaffald
Emissions of Quaternary Alkylam­monium Compounds
Nikotinposer – indhold og miljøkonsekvenser
Udredningsprojekt vedr. analysemetoder til undersøgelse for PFAS-forbindelser i jord, grundvand og overfladevand
Rensningsmuligheder for pesticider med fokus på aktivt kul og membraner
Renholds- og omkostningsanalyse jf. Engangsplastdirektivets oprydningsansvar
Kemiske stoffer i en cirkulær økonomi - Et MUDP projekt
Pesticider og biocider i den danske pindsvinebestand
Kortlægning af madaffald i primærproduktionen samt forarbejdnings- og fremstillingssektoren for 2022
Kortlægning af madaffald og madspild i restaurationsbranchen og restaurationstjenester for 2022
Inhibition of lung surfactant function as an alternative method to predict lung toxicity following exposure to plant protection products
Survey and risk assessment of pesticides in cut flowers from non-EU countries

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