APM: 503 Queue is full, server sleeping, nothing helps

APM does not keep logs at all

Do you mean that you have disabled keeping logs? By default the APM Server does write to log files.

I assume you might encounter a similar bug to what we have seen in another discuss entry (APM Failed to publish events: temporary bulk send failure / Queue is full 503 error).
From 7.4 on apm pipelines are enabled by default, and a new field client.ip is indexed. Providing invalid data for fields that are part of the pipelines, can lead to errors and ingestion retries. This seems to happen in some cases for 7.4 for the client.ip field. There is a bug fix for this, that will be part of the next patch release for 7.4.
Until then I suggest you disable the pipeline, and remove the client.ip field from being ingested. You can do so by changing your apm-servery.yml file to include following settings:

output.elasticsearch.pipeline: "_none"
processors:
  - drop_fields:
      fields: ["client.ip"]
      ignore_missing: true

Hope this solves your issues, apologies for the inconveniences.