Upd: I tried to set up SSL like it is described here
Now, the error message is different, and is similar to the one, mentioned here
[2023.03.09-17.18.49:421][210]LogOnlineIdentityEpic:Display: Epic login success.
[2023.03.09-17.18.49:421][210]LogOnlineIdentityEpic:Display: Epic Connect Login…
[2023.03.09-17.18.49:663][250]LogOnlineIdentityEpic:Display: Epic connect login success.
[2023.03.09-17.19.40:505][365]LogHttp:Warning: 0000019943D33F80: request failed, libcurl error: 7 (Couldn’t connect to server)
[2023.03.09-17.19.40:511][366]LogFuncomLiveServices:Warning: RepeatPlayFabClientRequest: Request timed out, scheduling a further attempt. (request type: struct PlayFab::ClientModels::FGetPlayerProfileRequest)
[2023.03.09-17.20.30:802][238]LogHttp:Warning: 00000199406D9E00: request failed, libcurl error: 7 (Couldn’t connect to server)
[2023.03.09-17.20.45:807][238]LogFuncomLiveServices:Warning: RepeatPlayFabClientRequest: Request timed out, scheduling a further attempt. (request type: struct PlayFab::ClientModels::FGetPlayerProfileRequest)
[2023.03.09-17.21.26:989][390]LogOutputDevice:Display: Bug report upload completed with result code 200, took 0.190 seconds.
[2023.03.09-17.21.36:085][201]LogHttp:Warning: 000001993282F3C0: request failed, libcurl error: 7 (Couldn’t connect to server)
[2023.03.09-17.22.07:096][ 13]LogFuncomLiveServices:Error: In RepeatPlayFabClientRequest: Request Timeout or null response RepeatPlayFabClientRequest: Request Failed. Exhausted all retries. (request type: struct PlayFab::ClientModels::FGetPlayerProfileRequest)
[2023.03.09-17.22.07:096][ 13]LogFuncomLiveServices:Error: In Login: Request Timeout or null response RepeatPlayFabClientRequest: Request Failed. Exhausted all retries. (request type: struct PlayFab::ClientModels::FGetPlayerProfileRequest)
[2023.03.09-17.22.07:096][ 13]LogFuncomLiveServices:Error: Login failed: Request Timeout or null response RepeatPlayFabClientRequest: Request Failed. Exhausted all retries. (request type: struct PlayFab::ClientModels::FGetPlayerProfileRequest).
[2023.03.09-17.22.07:096][ 13]ConanSandbox: Requested Message FlsLoginFailed. (Currently Active message FlsLoggingIn)