Template literal types were not inheriting validation tags when intersected with tags like MaxLength and Pattern. This caused validation to pass incorrectly when it should fail.

Problem

Consider this type intersection:

type TaggedTemplate = tags.MaxLength<10> & 
                     tags.Pattern<'^[a-zA-Z0-9_]+$'> & 
                     `prefix${string}postfix`;

const testValue = 'prefix;"+,df0123456789postfix'; // 28 chars, special characters

// Before fix: This would pass validation (incorrect)
typia.validate<TaggedTemplate>(testValue); // { success: true }

// But regular string with same tags would fail correctly  
typia.validate<tags.MaxLength<10> & tags.Pattern<'^[a-zA-Z0-9_]+$'> & string>(testValue); 
// { success: false, errors: [...] }

The issue affected all validation functions: validate, assert, is, and schema generation.

Root Cause

The intersection handler correctly processed validation tags and attached them to template literal metadata. However, the code generator for templates (check_template) was only generating pattern matching code and ignoring the tpl.tags field, unlike check_string which processes both type checking and validation tags.

Solution

Modified src/programmers/internal/check_template.ts to:

1. Add validation tag processing: Created check_template_type_tags function similar to check_string_type_tags
2. Generate validation conditions: Process tags with validate scripts and transpile them to runtime checks
3. Combine all validations: Return conditions that include template pattern matching AND validation tag checking

Updated call sites in CheckerProgrammer.ts and check_dynamic_key.ts to pass the required context parameter.

After Fix

// Now correctly fails validation
typia.validate<TaggedTemplate>('prefix;"+,df0123456789postfix');
// { 
//   success: false, 
//   errors: [
//     { expected: "string & MaxLength<10>", ... },
//     { expected: "string & Pattern<'^[a-zA-Z0-9_]+$'>", ... }
//   ] 
// }

// Valid values pass as expected
typia.validate<TaggedTemplate>('prefix123pos'); // { success: true }

The fix ensures template literals validate against:

1. Template structure (must match prefix*postfix pattern)
2. Length constraints (MaxLength<10>)
3. Pattern constraints (Pattern<'^[a-zA-Z0-9_]+$'>)

Fixes #1635.

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