A fellow Matrix user has reported that matrix.group.lt has stopped showing Youtube URL previews and suggested that according to GitHub - the issue lies with Synapse server software itself. So now I:

• have a rough idea of wtf is oembeds
• know that Synapse has an issue parsing https://oembed.com/providers.json
• know how to clean providers.json to work with Synapse (https://gist.githubusercontent.com/nycterent/e91c524288d24f8fbd05a81b8953d829/raw/90ef01739d5d274a2c887a3bdaa28ad7eb962102/oembedproviders.json)
• know how to configure matrix-docker-ansible-deploy to work with it:

in vars.yaml

matrix_synapse_configuration_extension_yaml: |
  oembed:
    disable_default_providers: true
    additional_providers:
     - /oembedproviders.json
  other_custom_config_blocks_for_homeserver

matrix_synapse_container_additional_volumes: 
  - {"src": "/matrix/oembedproviders.json", "dst": "/oembedproviders.json", "options": "ro"}  

you need to upload oembedproviders.json to the server first and then regenerate Synapse configs and restart it:

ansible-playbook -i inventory/hosts setup.yml --tags=setup-synapse,restart-all

Thank you, Citizen Laszlo for not ignoring the issue.