When you enable Active-Active mode on an Azure VPN Gateway, the gateway transitions from a single public IP with one active instance to two active instances, each with its own public IP. This change disrupts the existing BGP session because your on-premises router needs to recognize the new setup and establish BGP peering with both instances. The existing BGP connection moves from "Connected" to "Connecting" because your on-premises router may still be trying to establish a session with the old single-instance setup. To fix this, ensure your on-premises router is configured to support two BGP peers (one for each gateway instance) and update your VPN device to establish connections with both IPs of the active-active setup.
For your second scenario, enabling BGP on the VPN Gateway and selectively enabling it for two out of six connections should not impact the existing four non-BGP connections. Azure allows BGP and non-BGP connections to coexist on the same VPN Gateway. However, once BGP is enabled, the two BGP-enabled connections will begin exchanging dynamic routes, while the remaining four connections will continue using static routes. Ensure that your routing policies do not unintentionally override static routes with BGP-learned routes, which could affect traffic flow.
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hth
Marcin