Hello, I'm back. I tried to boot into "Try Zorin", it works the same way, i. e. simply doesn't work
Do you want to change your input system to XFCE FCITX and see if it make any difference?
XFCE FCITX is included as a default in Zorin OS.
Yup. Thanks for quick pointing out my mistake.
While I do not keep my hope high, I thought we would leave no stone unturned.
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Hello, I'm back, again
How should I change it to FCITX? I don't know honestly
It is already included in the system.
Can you open the Language support?
There is a drop-down list to change your input system at the bottom.
Change iBus to FCITX there.
Ah, sorry.
You are using Russian and I am using Japanese.
Obviously we do not have the same input system 
Oh, got it 
So the only way left is to find that one terminal command?
I went back to that GitHub page and read the instruction again:
Just to confirm.
You followed these instructions precisely, right?
Дождитесь зелёного сообщения об успехе. В процессе установки может потребоваться ввод пароля.
Обязательно перелогиньтесь после установки.
[edit]
I just saw from the screenshot you posted that Russian language support is not the first choice or not installed. Can you check this?
Yes, I did exactly as instructed
I installed the Russian language support, nothing changed
Do you see any FCITX as an input option now?
No, I don't
Did you select Russian as your first selection of language?
No, how to do that?
- Open Language and region.
- Select Russian language.
- Hold the selection and bring it to the top of the list of languages (just like in Mac, if you know it).
Sorry, I forgot to add one more step.
Click on
Manage Installed Languages.
Mine looks like this:
Mine has 日本語 on the top of the list.
Yours should have Russian on the top of the list.
OK.
Select that and hold your left mouse button to grub it and bring it up to the top of the list. You must go higher than English to make it enabled.