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

  const result = { ...base };

  for (const override of overrides) {
    const [name, value] = override.split('=', 2);
    if (typeof name !== 'string' || name.length === 0) {
      throw new Error("override must have a non-empty name");
    }
    if (typeof value !== 'string') {
      throw new Error("override value must be a string");
    }
    if (!result.hasOwnProperty(name)) {
      throw new Error(`base does not contain setting: ${name}`);
    }
    result[name] = value;
  }

  return result;
}
```