I tried with all HTTP methods enabled for /api/user only, and it update user successfully.
But if I tried only with GET and PATCH methods enabled for /api/user , I get 'statusCode=401'.
Here is code
import { FusionAuthClient, UserRequest } from '@fusionauth/typescript-client'
...
export class FusionAuthService {
    private fusionAuthClient: FusionAuthClient;
    constructor(private context: Context) {
        this.fusionAuthClient = new FusionAuthClient(context.config.fusionAuth.apiKey, context.config.fusionAuth.apiUrl);
    }
...
    public async updateUser(userId: string, userRequest: UserRequest ) {
        return this.fusionAuthClient.updateUser(userId, userRequest)
            .then(clientResponse => {
                logger.info("User:", JSON.stringify(clientResponse.response.user, null, 2));
            }).catch(logger.error);
    }
here is invocation of updateUser method that happens on 'user.registration.create' event
        if (user) {
            const patchBody = {
                user: {
                    email: event.user.email,
                    data: {
                        userId: user.id
                    }
                },
            }
            await this.fusionAuthService.updateUser(event.user.id, patchBody);
        }
Now I understand that I use updateUser method and I don't know what kind of HTTP request it used.
I have found  patchUser and with it get success.
Thanks for your help.