```typescript
export function applyOverrides(base: Record<string, string>, overrides: string[]): Record<string, string> {
  if (!Array.isArray(overrides)) {
    throw new Error("overrides must be a list");
  }

  const merged = { ...base };

  for (const override of overrides) {
    const [name, value] = override.split('=', 2);
    
    if (!override || name === '' || !value) {
      throw new Error("Each override must be a non-empty string with an equals sign");
    }

    merged[name] = value;
  }

  return merged;
}
```