Traffic between two switch ports doesn't even exit the other switch ports, so it won't even arrive at the router.
If there is nothing else going on (no DNS lookups, for example) then there will be nothing but traffic across the switch. You can assign long leases for infrequent DHCP traffic to the router; or indefinite leases for once-per-boot. DHCP, ...
Yes. You don’t even need a trunk. If all ports on both switches are access ports on Vlan 3, then the port connecting the two switches are on Vlan 3 and both switches form one broadcast domain on that Vlan.
If switches are unmanaged then all ports would be on the one Vlan and the number is irrelevant.
A couple helpful details:
Access ports to end hosts or ...
Without VLANs, connected switches form a single broadcast domain - that is exactly what you need for an IP subnet. Just connect away.
VLANs allow you to split (partition) a shared switched infrastructure into distinct broadcast domains - ideally suited for multiple IP subnets. In order to connect multiple VLANs across a single link you'd need a trunk, ...
I used NXM_NX_IPV6_DST field and load action to resolve this problem on openvswitch bridge by adding a flow
ovs-ofctl -O openflow13 add-flow br0 "priority=60000,ipv6,ipv6_dst=2020::/16,actions=load:0x2010->NXM_NX_IPV6_DST[112..127]"