No more api connection from deep-sleep sensor after HA Core 23.8.0 upgrade

I have a weather station that wakes up every 10 minutes and uses api to transmit values. Worked over months without problems and no changes to code have been done (just new compilations when new esphome versions have been published).

Yesterday I updated HA to 23.8.0 and now the sensor does not report back. I get this log entry.

[10:42:10][W][component:204]: Component api took a long time for an operation (0.28 s).
[10:42:10][W][component:205]: Components should block for at most 20-30ms.

Does this mean HA is responsing to slow? But other deep-sleep sensors connect without problems.
I already increase the timeout which waits for api connection:

- wait_until:
    timeout: 15s

increased it to 60s. Same failure. I tried another esp8266 with same code flashed. Same problem. What could be the reason that an upgrade to HA Core would affect my sensor?

Any ideas?