The latest version of the integration allows using displays without the OpenEpaperLink gateway. You need to have a Bluetooth adapter in your Home Assistant server, ESPHome gateways, or Shelly devices around the house to have Bluetooth gateway.
You need to flash the displays with the custom firmware from atc1441.
Download the bin file from: atc1441.github.io/ATC_BLE_OEPL.bin at 1c4833b4ed8d8afbbbb2bc88f337acf151a40348 · atc1441/atc1441.github.io · GitHub
Open Telink BLE E-Paper Flasher, connect to your display and flash it (select the bin file you downloaded)
Open: ATC_BLE_OEPL Uploader, connect to the device, go to Advanced View (top right corner of the page) and set device type:

Update the integration to the latest version (version 2.1.0 currently).
Tested displays:
GICIsky 2.9 inch display: https://s.click.aliexpress.com/e/_c3Dj4YsP
GICIsky 4.2 inch display: https://s.click.aliexpress.com/e/_c4LefB1N
Both of them have been tested and they work without any problems.
The display update time is much better - the display reacts almost instantly as you call the service. Before, I had to manually reset the gateway once a week, because the displays stopped refreshing; now the problem doesn’t occur as the gateway is obsolete.