I found a working solution to the problem mentioned above.

It only works if you own the page and have access to Facebook Business Manager. In that case you can create a system user and generate a system user access token. This token can be granted the necessary permissions for the page and, crucially, does not expire (unless the permissions will be changed or revoked).

Steps:

1. Set Up Facebook Business Manager: Go to business facebook manager and create a Business Manager account if you don’t already have one.

2. Add your Facebook page to your Business Manager.

3. Create a Facebook App: In the facebook developer portal create a new app (or use an existing one).

4. Add a System User: In Business Manager, navigate to Business Settings > Users > System Users. Click Add to create a new system user (give it a name and assign it a role, usually "Admin" for full access).

5. Assign Assets and Permissions: Assign your Facebook page as an asset to the system user.

6. Grant the system user the necessary permissions for the page.

7. Generate a System User Access Token: In the system user’s settings, click Generate New Token. (Select your app and the required permissions.)

8. Use the System User Access Token to generate a System Page Access Token