You might not see this feature yet. Some functionality is introduced gradually to organizations that have set up the Targeted release options in Microsoft 365.
I...
(for some reason I replied twice but neither one got posted, so, I'm going to try this again)
So sorry, Matt but I am well aware that "Save as Site Template" or "save as list template" have been around since WSS 3.0 (or possibly earlier). But, this option is no go in SPO for modern sites. I tried and no you cannot do so according to the article http://webbrewers.com/modern-sharepoint-create-a-site-template-yes-communications-sites-too/ . The /_layouts/15/savetmpl.aspx will NOT work (see screenshot from my tenant).
Microsoft introduced Site Scripts and Site Designs as a way to automate provisioning new or existing modern SharePoint sites that use your own custom configuration. And, now (according to this article) Microsoft, once again, will refer to Site Designs as Site Templates. And, so far, even though I have setup targeted release, I still do not see the option of "Apply a Site Template" yet in my tenant.
Therefore, my original question still stands: I'm still trying to understand how this new "site template" is different than "Site Designs". Will it allow us to create a template like it did in earlier versions of SP similar to "Save site as template"?