The below code iterates all the template definitions from the template library recursively on each category and prints the template names.

//Required References
using System;
using Bentley.CifNET.GeometryModel.SDK;
using System.Diagnostics;

 public void ListAllTemplatesInTemplateLibrary()
        {
            try
            {
                //Get template library path
                string strTemplateLibraryPath = Bentley.CifNET.GeometryModel.SDK.TemplateLibrary.GetDefaultTemplateLibraryPath();

                //Get template library
                Bentley.CifNET.GeometryModel.SDK.TemplateLibrary templateLibary = Bentley.CifNET.GeometryModel.SDK.TemplateLibrary.Load(strTemplateLibraryPath);

                //get root category from template library
                Category rootCategory = templateLibary.RootCategory;

                //Iterate to find templates
                RecursivelyFindTemplates(rootCategory);
            }
            catch (Exception ex)
            {
                Trace.WriteLine(ex.Message);
            }
        }

        private void RecursivelyFindTemplates(Bentley.CifNET.GeometryModel.SDK.Category parentCategory)
        {
            foreach (var category in parentCategory.Categories)
            {
                //Recursively iterate categories for finding templates
                RecursivelyFindTemplates(category);
            }

            //Iterate each template definition from current catergory
            foreach (var template in parentCategory.Templates)
            {
                Trace.WriteLine(template.Name);          
            }
        }

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Output