Yes, you're correct The ExpressRoute Gateway will learn all AVS routes via the ExpressRoute connection. Since you have an iBGP session between the ER Gateway and the Azure Route Server, those AVS routes will also be propagated to the Route Server.
The Route Server will then advertise those routes to any connected BGP peers (like NVAs or other gateways).
The ER gateway learns routes from the on-premises network via BGP over the ExpressRoute circuit.
The ER gateway exchanges routes with the Microsoft Enterprise Edge (MSEE) routers using eBGP for private peering. The AVS routes advertised to the MSEEs are propagated to the ER gateway, and you can view these routes using the Get-AzVirtualNetworkGatewayLearnedRoute Azure PowerShell command. These routes will include the AVS /22 network prefixes.
2.Incoming Traffic to AVS to Next Hop: This depends on where the traffic originates and where you're inspecting the route:
From On-Premises to AVS:
- Next Hop in Route Table:
- In on-prem routers: next hop is MSEE
- In ER Gateway: next hop is AVS internal IP
- In Route Server: next hop is ER Gateway From Azure VNet Peers to AVS:
- If the VNet is peered and routes are propagated via Route Server
- Next hop will be ER Gateway, as it’s the bridge to AVS.
Sharing similar thread which will be helpful for you https://learn.microsoft.com/en-us/answers/questions/1741721/routing-tables-on-express-router-and-virtual-netwo
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