I've made a Google Sitemap Tree, ie linking child xml files to the main xml. However, Google Search Console shows that 0 pages are discovered for the parent sitemap xml. Is Google Search Console not finding the URLs in the child xml files or is this normal?
It isn't normal - GSC should be showing the total number of discovered URLs found next to this parent sitemap, and once you click on it, then it should show each individual sitemap with their respective URLs found.
My guess is that there's something wrong with this parent sitemap file - have you tested using online tools? How about using the "live test" feature inside GSC?
Yes, it is normal. Because if you create a sitemap tree, you should make the sitemap on the top level as Sitemap Index, which contains all other nested sitemaps. The markup of sitemap index is different then of single sitemap. Look:
Sitemap Index (contains sitemaps!)
<?xml version="1.0" encoding="UTF-8"?> <sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"> <sitemap> <loc>http://www.example.com/sitemap1.xml</loc> </sitemap> <sitemap> <loc>http://www.example.com/sitemap2.xml</loc> </sitemap> </sitemapindex>
Sitemap (contains URLs!)
<?xml version="1.0" encoding="UTF-8"?> <urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"> <url> <loc>http://www.example.com/foo.html</loc> <lastmod>2018-06-04</lastmod> </url> </urlset>
More details here.