It is a bit confusing.
A channel can be published as a Direct Publisher channel or an SDK channel - it can't be both.
Having a live / published channel doesn't mean that the channel will show up in search results.
If you have an SDK channel, you can build and submit a search feed - it is kind of the only way to make sure your content is searchable - after approval and ingestion, your content can be searched.
But at any time, you can share your Roku Channel Store URL with your viewers and ask them to install the channel that way.