Is it possible to use this adapter to connect TB2 MacBook to a TB4 docking station?

I would like to find a solution to connect an old MacBook Pro 13" to a new Thunderbolt 4 docking station. It seems a lot of people try this and, after spending tons of money, give up.

Here's the setup:

• MacBook Pro 13.1" ca. 2013 buld with two Thunderbolt 2 ports on the side
• The so-called "bi-directional" TB2 to TB3 adapter from Apple
• A 0.5m Thunderbolt 2 cable.
• A Lenovo TB4 docking station 40B00135UK model

I am not trying to connect a USB-C device to a Thunderbolt port. This is a Thunderbolt 2 to Thunderbolt 4 connection. In theory thanks to having "backward compatibility" of Thunderbolt standards and a "bi-directional" adapter this should be perfectly possible. However the Thunderbolt Tree view shows nothing.

Do I need to throw out my high powered albeit old MacBook laptop just because there is no cable I can buy to make this work?