Will an active USB hub work with an active 10m USB cable?

Question

Cables and wires

Good day to all! I know that this topic has already been discussed many times on other resources, but I did not find the answer to my question.
The task is typical: a computer is in one room - a TV in another. I want to be able to play on the TV (having connected the joystick) or control the computer using the TV as a monitor. The distance between two points is 8 meters. I saw (and even ordered, just in case) USB - RJ45 - USB adapters. But, unfortunately, no matter how much I searched, I could not find such adapters that support USB 2.0, and those that I found cost unreasonable money - from $ 50.
Then I came across long active USB cables with an amplifier on one end:

There are many places where they write that they are not recommended for use, for something more energy-intensive than a mouse, which also does not suit me very much. Therefore, I had the idea to make the following connection:
PC - USB cable - active USB hub (plugged in) - USB devices.
Thus, it will probably be possible to compensate for the energy loss of the cable itself. Tell me, please, has anyone tried a similar connection? Will it work?