Strictly speaking it’s not a Router on a Stick scenario as you have the WAN direction there.
As you say the switches host non-overlapping sets of VLANs, there is actually no need that you bridge together their connections to the routers at the router end, you can connect SW1 to eth2 of RT1 and SW2 to eth3 of RT1, and attach the vlan “subinterfaces” for VLANs handled by SW1 to eth2 and the vlan “subinterfaces” for VLANs handled by SW2 to eth3.
The situation would be different if you wanted to connect also some LAN hosts to the same VLAN on two different switches for redundancy purposes - in that case, you’d have to bridge the eth2 and eth3 together at each router, and use STP to prevent L2 loops.
Is the above an answer to your question?
The biggest issue with this kind of setup is if the routers should also act as stateful firewalls - you can use VRRP at the LAN side, but synchronisation of connection tracking is only available in RouterOS 7.x, which is still far from production-grade stability. As an alternative, there’s the High Availability setup by @nathan1 which takes a completely different approach, where the complete configuration is mirrored between the two routers (which must be identical models).