Update examples to use `adafruit_connection_manager`

I already updated the Ethernet example, but other examples could use `adafruit_connection_manager` to simplify the code and make it more uniform among the examples.

Note that `docs/starting_methods.rst` will need to be updated, as it points to specific line numbers.

Compare the remaining examples with the already updated Ethernet example and identify which still use the older connection setup. Update those examples to use adafruit_connection_manager, then update docs/starting_methods.rst so its referenced line numbers remain accurate. Done means the examples are uniform and the documentation links to the correct lines.

Written by the indexing model from the issue text.