For anyone who comes across this problem, it apparently it is resolved (by stopping the client in EMailSender::send) already in EMailSender 2.4.3. Note, however, that with Arduino IDE 1.X (I don't know about 2.X), the installed library with the IDE's library manager is v2.4.2, which still has the problem. You have to manually download the 2.4.3 library and place it in the ardiuno include library directory.
From the change log in EMailSender v2.4.3:
Change log
- 12/04/2021: v2.4.3 Fix multiple email send
- 12/04/2021: v2.4.1 Add support for LITTLEFS and Ffat on esp32 and fix certificate verification from esp32 core 1.0.5
- 18/03/2021: v2.3.0 Add support for LittleFS on esp8266
- 02/01/2021: v2.2.0 New support for SAMD devices via WiFiNINA (Arduino MKR WiFi 1010, Arduino Vidor 4000 and Arduino UNO WiFi Rev.2 ecc.).
- 01/01/2021: v2.1.5 Add possibility to use EHLO instead of HELO, and SASL login.
- 27/11/2020: v2.1.4 Add more constructor to allow more structure for distribution list (now const char*, char* and String array are supported)