Two way data binding and sending data from html to variables in ts file

Identifier 'password' is not defined. The component declaration, template variable declarations, and element references do not contain such a member

because it unable to find those two variables in TS file, use this:

HTML file .

<p class="lead">Already a member? Please <a routerLink="/login">log in</a> instead</p>
    <form (submit)="onRegisterSubmit()">
    <div role="alert" *ngIf="formError" class="alert">{{ formError }}</div>
          <p>
              <label>Email</label>
              <input type="text" [(ngModel)]="email" required>
          </p>
          <p>
              <label>Password:</label>
              <input type="password" [(ngModel)]="password" required>
    
          </p>
          <p>
              <button type="submit" >Submit</button>
          </p>
      </form>

.TS file

import { User, UserRegister } from './../user';

import { Component, OnInit } from '@angular/core';
import { NgModule }      from '@angular/core';
import { BrowserModule } from '@angular/platform-browser';
import { FormsModule } from '@angular/forms';
import { Loc8rDataService } from '../loc8r-data.service';
import { Router } from '@angular/router';
import { AuthenticationService } from '../authentication.service';



@Component({
  selector: 'app-register',
  templateUrl: './register.component.html',
  styleUrls: ['./register.component.css']
})

    export class RegisterComponent implements OnInit {
    
      constructor(private Authentication: AuthenticationService) { }
    
      
      ngOnInit() {
      }
      password:string='';
      email:string='';
        
    
      formError: string ='';
    
        public onRegisterSubmit(): void {
    
        this.doRegister();
       
          }
    
        private doRegister(): void {
    
          let uEmail = '';
    let uPassword = '';
    const userreg: UserRegister = {email: uEmail, password: uPassword };
    
        this.Authentication.register(userreg)
        .catch((message: string) => this.formError = message);
    
        }
    
    }

See the following for added description. But you are just using incorrect syntax. See below.

https://angular.io/guide/two-way-binding

https://angular.io/guide/built-in-directives#ngModel

You don't need the braces

 <input type="password" [(ngModel)]="{{password}}" required>

should be

 <input type="password" [(ngModel)]="password" required>

Be sure that you have declared any variable that you are using in your html template inside your .ts file as a public field or your html file will not be able to use it.