High-availability configuration produces a status of "ONLINE (STANDBY), In Sync"

Usually if there would be an issue with communication channel you would end with Active-Active state - not a Standby-Standby.

• step 7 - check if network failover checkbox is marked
• verify if your device-group includes both devices (on the left side)
• check /var/log/ltm for high availability status. Look for "Active" and "Standby" messages

You can try to reset trust and setup HA again as per: https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-implementations-11-5-0/2.html