HTTPS Custom API session broken during TLS handshake

I cannot make Nettigo Air Monitor (KIT BME 0.3.3 STD language EN) post data to my own API.

Configuration: Firmware - tried with NAMF-2020-46rc2 (and before also the stable release).

Actual results:

Does not post the data to the server. The session is disconnected from the client side during the TLS negotiation.
Debug log "Not succeeded. HTTP status code: -1"

Expected result:

Additional info:

I can access my own API server with other means - e.g., postman and curl.
The sensor can post the results to API Sensor Community and Madavi.de. Both with https.
I've debugged the network traffic. The Client and the Server agree on TLS 1.2 / TLS_RSA_WITH_AES_128_CBC_SHA256 cipher. The connection goes until "Server Hello Done". Then is disconnected from the client side (sending FIN, ACK packet flag). (I use RSA 2048 certificate for the server. The server is facing AWS CloudFront.)
The sensor also fails to post the results to pipedream.net when port 443 is selected. It does post on port 80.

Here is the debug of the connection:

Idea:

Is the processor strong enough for the cipher? Don't we have to use less CPU/memory-intensive cipher? There are four ciphers available if option BEARSSL_SSL_BASIC is set (see https://github.com/esp8266/Arduino/blob/master/libraries/ESP8266WiFi/src/WiFiClientSecureBearSSL.cpp#L931). Could be that not all of them work for ESP8266?
api.sensor.community uses TLS 1.2 / TLS_RSA_WITH_AES_256_CBC_SHA256. The same cipher is used for api-rrd.madavi.de.

Here is the Server Hello packet from api-rrd.madavi.de (i.e., it works):

Here is the Server Hello packet from pipedream.net (i.e., it does not work):

nettigo / namf