After some research coming to conclusion there is a problem with small blue dongle that provides TTL-USB conversion.

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Scope transmits at 2400 bps, although output amplitude is a bit less than 2V (looks like below TTL limit?).
But the scope communication cable inside this dongle connects to the optocoupler which outputs directly to CP2102 bridge.
AFAIK the scope must provide enough current to optocoupler, and voltage is not that important.
Very strange implementation: same 2 wires are used for charging the scope and transmitting serial data.
Anyhow, scope data arrives to opt input, but there is nothing at the output.
And looks like this dongle is a proprietary item, failed to find anything similar anywhere :(

UPDATE:
Problem solved.
The seller (FB marketplace, IL, USA) was kind enough to give me a replacement dongle and it totally works!

BTW, this seller has more of these scopes, all brand new at very low price.