Is it possible to have a notification displayed whenever any integration fails or stops working?
I usually check entities created by an integration for presence. Assume there are 3 sensors named “sensor.xyz_*” created by XYZ integration. So check these 3 entities for presence on HA startup. Also you may want to check these entities for “unavailable” periodically.
Of course, you can create blueprints for these operations and then create automations for each monitored integration and corresponding name pattern.
PS. If course these automations should notify you about results using either persistent notifications or smth like Telegram.
My notifications usually appear in the system error log when there are issues.