What is the most recent version of the ESPHome used as HA addon ?
Mine is v2022.3.1
I could see many newer releases incl. 2022.10.0 on ESPHome web page.
Is it like the addon version is simply older or I should take a closer look on update mechanism in my HA ?
There was a breaking change about March-April.
You need to replace the addon.
Hah, I thought sth. is wrong 
Thanks
Is the operation that easy like remove and re-add the addon ?
Would it preserve my devices or I would need to readd them ?
Go back and read or do a backup.
I don’t know.
Just checked.
It’s enough to uninstall add-on and install it again.
Not touching the integration preserved all devices.
Thanks.