Add Spelling Bee and connections support to NYT Games (#126567)

homeassistant/components/nyt_games/coordinator.py

homeassistant/components/nyt_games/entity.py

homeassistant/components/nyt_games/icons.json

homeassistant/components/nyt_games/sensor.py

homeassistant/components/nyt_games/strings.json

tests/components/nyt_games/conftest.py

tests/components/nyt_games/fixtures/connections.json

tests/components/nyt_games/snapshots/test_init.ambr

tests/components/nyt_games/snapshots/test_sensor.ambr

tests/components/nyt_games/test_init.py

tests/components/nyt_games/test_sensor.py