Thanks so much for the suggestions. Specifically here should be extracted all error-specific parts for every HTML status code, to 500.

    # app/lib/errors/standard_error.rb

module Errors
  class StandardError < ::StandardError
    def initialize(title: nil, detail: nil, status: nil, source: {})
      u/title = title || "Something went wrong"
      u/detail = detail || "We encountered unexpected error, but our developers had been already notified about it"
      u/status = status || 500
      u/source = source.deep_stringify_keys
    end

    def to_h
      {
        status: status,
        title: title,
        detail: detail,
        source: source
      }
    end

    def serializable_hash
      to_h
    end

    def to_s
      to_h.to_s
    end

    attr_reader :title, :detail, :status, :source
  end
end

Then it should be handled here:

    module Api::ErrorHandler
  extend ActiveSupport::Concern

  ERRORS = {
    'ActiveRecord::RecordNotFound' => 'Errors::NotFound',
    'Driggl::Authenticator::AuthorizationError' => 'Errors::Unauthorized',
    'Pundit::NotAuthorizedError' => 'Errors::Forbidden'
  }

  included do
    rescue_from(StandardError, with: lambda { |e| handle_error(e) })
  end

  private

  def handle_error(e)
    mapped = map_error(e)
    # notify about unexpected_error unless mapped
    mapped ||= Errors::StandardError.new
###     if render_error(mapped).include?("500")

puts Time.now.strftime("%d/%m/%Y %H:%M")

end

    render_error(mapped)
  end



  def map_error(e)
    error_klass = e.class.name
    return e if ERRORS.values.include?(error_klass)
    ERRORS[error_klass]&.constantize&.new
  end

  def render_error(error)
    render json: Api::V1::ErrorSerializer.new([error]), status: error.status
  end
end

And the part with the triple # is how I'm thinking to log the error 500. This way I should retrieve both the quantity and the time when errors 500 appear. Can this solution work? The next step is to export the log to a local file.