Here are a couple of suggestions

Non default CRUD action in Controller

It's generally recommended to only have CRUD actions index, show, new, edit, create, update, destroy in your controllers. So e.g. you should think about renaming your register and login actions and extract according controllers.

For example you could have a UserRegistrationsController and a UserLoginsController which each have a create action.

class V1::UserRegistrationsController < ApplicationController
  def create
  end
end

class V1::UserLoginsController < ApplicationController
  def create
  end
end

Here is a good blog article explaining this concept http://jeromedalbert.com/how-dhh-organizes-his-rails-controllers/

Handling user not found

Instead of using find_by you could use the bang method find_by! which will raise a RecordNotFound error.

User.find_by!(email: params[:email])

Now RecordNotFound errors will get automatically translated to a 404 response code. But you could overwrite the default behaviour as well with your own exception app or rescue_from

https://github.com/rails/rails/blob/main/actionpack/lib/action_dispatch/middleware/public_exceptions.rb#L14 https://stackoverflow.com/questions/62843373/how-to-deal-with-general-errors-in-rails-api/62846970#62846970

Another possibility is to add a validation with scope so you can only have one email address.

class V1::UserRegistrationsController < ApplicationController
  def create
    @user = User.new(
      name: name,
      email: email,
      password: password,
      plan: "FREE"
    )

    if @user.save
      render @user
    else
      render @user.errors
    end
  end

Strong parameters

User strong parameters instead of plucking the values from the params hash.

der user_params
  params.require(:user).permit(:email, :password, :name)
end

https://edgeguides.rubyonrails.org/action_controller_overview.html#strong-parameters

Use a PORO or Service object

A lot of people will have different opinions of using a Plain Old Ruby Object vs a Service object etc. But I think a lot of people would agree that it's a good idea to move logic from the controller to a dedicated object.

Example

class UserRegistration
  def self.create(params)
    new(params).save
  end

  def initialize(params)
    @params = params
  end

  def save
    user = create_user
    auth = UserAuth.new(
        access_token: generate_token,
        user_id: user.id,
        status: true
    )
    auth if auth.save
  end

  private

  attr_reader :params

  def create_user
    User.create(
      name: params[:name],
      email: params[:email],
      password: params[:password],
      plan: "FREE"
    )
  end

  def generate_token(size = 28)
    charset = %w{ 2 3 4 6 7 9 A C D E F G H J K M N P Q R T V W X Y Z}
    (0...size).map{ charset.to_a[rand(charset.size)] }.join
  end
end

And then you can just do in your controller

class V1::UserRegistrationsController < ApplicationController
  def create
    if (auth = UserRegistration.create(params))
      render auth
    else
      render :error
    end
  end
end

Generally speaking I think there is too much logic in your controllers which makes it hard to read and test.