The templates command provides information about existing templates.

GET /_cat/templates?v&s=name

which looks like

name      index_patterns order version
template0 [te*]          0
template1 [tea*]         1
template2 [teak*]        2     7

The output shows that there are three existing templates, with template2 having a version value.

The endpoint also supports giving a template name or pattern in the url to filter the results, for example /_cat/templates/template* or /_cat/templates/template0.