[nextion] Replace connect_info vector with fixed-size field parser, always log device info (#16059)

Co-authored-by: pre-commit-ci-lite[bot] <117423508+pre-commit-ci-lite[bot]@users.noreply.github.com>

tests/components/nextion/common.yaml

@@ -276,7 +276,6 @@ display:
     auto_wake_on_touch: true
     brightness: 80%
     command_spacing: 5ms
-    dump_device_info: true
     exit_reparse_on_start: true
     lambda: |-
         ESP_LOGD("display","Display is being tested!");