Azure ExpressRoute - Cisco Meraki MX or directly into LAN?

For the design you described, I would plan on dedicated CPE in front of the Meraki environment. ExpressRoute with provider Layer 2 handoff, VLAN tagging, BGP, and routing policy usually needs a router or firewall platform that gives you much more control than a Meraki MX normally provides.

I would not terminate this directly on the LAN switch unless that switch is intentionally acting as the routed edge and supports the VLAN and BGP features your provider requires. A cleaner pattern is to terminate the ExpressRoute private peering on dedicated routers, apply the route filtering and advertisements there, and then hand the routes toward the Meraki side in a simpler way. That keeps the ExpressRoute-specific complexity out of the SD-WAN edge.