Routing between two networks via VPN. Where does this behavior come from?

Question

VPN

There is a LAN with a Bintec-Elmeg be.ip Plus router (this is such a German beast that works correctly with a local ALL-IP business connection from Deutsche Telekom). Local has a network 192.168.5.0/24.
It must be connected via VPN to a branch in Russia. I can only control the setup in Russia to a limited extent, ie. "throw everything out and put the right hardware" is not an option.
After long dances with a tambourine and dancing, I managed to set up an IPSec IKEv1 VPN tunnel, which correctly connected my be.ip Plus with a Zyxel USG 300 not to a party in Russia. This ZyXEL has the address 10.10.10.1, and after one intermediate hop, it roots to the grids 192.168.1.0/24, 2.0/24, 3.0/24. On my side of the tunnel, I raised 10.10.10.5, respectively, and registered ruting to 192.168.1-3.0/24 through the tunnel.
But then some complete misunderstanding begins with roofing felts, roofing felts with firewalls, of which there are already 3 pieces between them. From my network, I can easily ping 10.10.10.0/24. My entire network (192.168.5.0/24) is pinged from Russia, but at the same time I myself cannot reach the 192.168.1-3.0/24 I need. And there is also such an anomaly: if you ping some device in my network from Russia and at the same time start ping back from this device, then it suddenly appears.
Help to understand, dear network gurus. I've been struggling with this problem for 2 days now.

Answer 1

And there is such an anomaly: if you ping some device in my network from Russia and at the same time start ping back from this device, then it suddenly appears.

The symptoms are very similar to a problem with a tunnel, or with a stateful firewall, look in this direction.