The node search indexes all nodes, and allows all of them to be searched by anyone. There are reasons to disallow nodes of certain bundles (i.e., content tyeps) to be searched, such as when those nodes do not have canonical pages.
There are two possible ways to do this:
a) Restrict certain content types from getting into the index in the first place.
b) Index everything, but at query time, filter the query to certain node types.
This issue is about (a).
(b) can be done in a contrib module, using something similar to the patch that was attached in comment #102 (see issue, which was marked as a duplicate of this issue). Custom modules can also accomplish this for a particular site by doing a query alter. They can look for queries with the 'search_node' query tag, and implement hook_query_TAG_alter() to alter the query.
Related contrib projects that did something similar to (b), at least in Drupal 7 versions:
Figure out how to do this in a consistent way, given that there can be multiple NodeSearch pages.
User interface changes
Data model changes
Probably there would be new config for this.