I just got the beta client version 1704760224 and see from the patch notes that this is fixed now.
I tested with CS2 and Euro Truck Simulator 2 and in game links open as expected when the restore option is either enabled or disabled.
When restore tabs is enabled, then previous tabs are correctly restored too as long as the overlay browser window was still open when exiting the game.
Nothing extracted yet.
Your system information
By default now steam client restores your browser tabs when opening the in game web browser. But if you turn off the option to restore your tabs then it will always force only the home page to be loaded and ignore any URL sent by the current game.
If the "Restore my previous browser tabs when starting a game" option is enabled then it will correctly open the URL requested by the game, in addition to previous tabs. (Sometimes it seems to forget any previous tabs though)
Steps for reproducing this issue: