Posting here in case somebody needs something similar:
Having this in hassio…
How to get informed on your phone?:
First I created a log file that saves every persistent notification that creates home assistatn to a log file. This is taken from VDRainer from here:
That is not needed. I did that to have a record with all notification events, which is always nice to have.
I use splitted configuration files to keep codes organized so, adapt for your case:
###/notify/notify_files.yaml
- name: persistent_notification_to_log
platform: file
filename: persistent_notify.log
…and for the automation that saves the file:
###/automations/automations_global.yaml
### PERSISTENT NOTIFICATION TO FILE:
- id: 'save_my_persistent_notifications_to_file_0937700372861'
alias: Save my persistent notification to file
trigger:
- platform: event
event_type: call_service
event_data:
domain: persistent_notification
service: create
action:
- service: notify.persistent_notification_to_log
data_template:
message: >
{{ now().strftime('%Y-%m-%d %H:%M:%S') }}
{{ trigger.event.data.service_data.title }} /
{{ trigger.event.data.service_data.message }}
I added an automated process that trims the log file daily to a maximun of 200 lines of text:
###shell_commands/shell_commands_global.yaml
trim_to_200_lines_the_persistent_notifications_log: ssh [email protected] -p 22 -o StrictHostKeyChecking=no -i /my_keyfile 'MYTMP=$(tail -n 5 /usr/share/hassio/homeassistant/persistent_notify.log 2>/dev/null) && echo "${MYTMP}" > /usr/share/hassio/homeassistant/persistent_notify.log'
(note: for my shell commands from hassio, I use to do an ssh out to self linux to take adventages of my already configured paths, commands, etc that’s because I always have had many problems when using the hassio internal shell directly. Not sure if it is a good way of executing commands, but that’s what works for me. Of course you have to check that you can ssh from hassio terminal to your native shell to execute the command (accept keys, etc, of first login).
…now the automation to trim the log daily a t 13:39:43 
###/automations/automations_global.yaml
- id: 'trim_to_200_lines_daily_the_persistent_notifications_log_2336478374673'
alias: Trim to 200 lines daily the persistent notifications log
trigger:
platform: time
at: '13:39:43'
action:
service: shell_command.trim_to_200_lines_the_persistent_notifications_log
(You can start here for only the telegram part)…now the automation that sends a telegram when a persistent notification, containing a matching string, is received:
###/automations/automations_assistants.yaml
- id: 'send_telegram_when_alexa_authorization_is_needed_3562223673560'
alias: Send telegram when Alexa authorization is needed
trigger:
- platform: event
event_type: call_service
event_data:
domain: persistent_notification
service: create
condition:
### CHECKS IF THE NOTIFICATION IS FOR AUTHORIZING AN ALEXA DEVICE:
condition: template
value_template: >
{{ 'Reauthenticate' in trigger.event.data.service_data.message }}
action:
- service: notify.telegrams_to_myself
data:
message: "Alert!. Notification at hassio to re-authorize Alexa, today at {{ now().strftime('%H:%M') }}"
Important thing to have in mind is that the text to be triggered from the persistent notification (‘Reauthenticate’ text in my case for alexa notification) MUST be part of the body of the notification (the small characters), not the bigger font of the title. That’s important because if you search for a string in the title, it will never trigger the alert. It doesn’t have to be just one word… it could be more like ‘Reauthenticate on the Integrations page’.
…of course, you need the notify service for telegram already configured, something like:
###/configuration.yaml
telegram_bot:
- platform: polling
parse_mode: html
api_key: 9876543210987654321abcdefghijklmnopqrstuvw
allowed_chat_ids:
- 123456789
and the notify entry:
###/notify/notify_telegram.yaml
- name: telegrams_to_myself
platform: telegram
chat_id: 123456789
Configuration → server_controls → Check_configuration button and → if green ok, then → restart_server.
You don’t have to wait for an Alexa authorize message to see if your automation triggers the text string you configured… you could just test with:
Developer Tools → Services → Service: persistent_notification.create → and paste this code to simulate an alexa authorization notification request:
###paste it in the service data field:
{
"title": "Sample notification",
"message": "test... Reauthenticate on the Integrations"
}
…and press CALL SERVICE button.
If everything went well, you will see that you phone receives a telegram notification of the alexa addon event.
Hope it helps somebody.