I've got some news!
I took my laptop to service and got it back today.
No issues with ports.
They had tested it with several devices and it passed all Apple tests.
There was note that some users have had these issues with LG usb-c displays.
Right ports uses different chipset to drive display and atm nothing can be done for this problem.
Only option is to wait firmware update from Apple or display manufacturer and there is no part to replace that could fix the problem.
That's not my case. I was using the display with the ports on the right side – it just stopped working. My 4K TV doesn't work too (on the right side).
My USB3 disk is rarely detected on the right side, and if it is detected, with USB2 speed (up to 480 mb/s).
I have 2018 Macbook Pro at work – everything is fine with the right side.