Moving layer 3 to another switch, what about spanning-tree

in CCNP
So I'm moving 2 3 layer VLAN interfaces to another switch to separate 2 customers and I was wondering If I need to do anything with spanning-tree, like change the root bridge for spanning tree. The current bridge has multi VLAN interfaces en is RB.
I'm wondering If I'm overthinking thing as I'm thinking the layer 2 path and 3 path need to point to the same root bridge/Layer 3 gateway.
So If I move another customer (move VLAN interfaces) of the RB, do I need to make the new switch RB for the newly configured VLAN interfaces?
Attached 2 pictures of the current situation and the new situation.
I'm wondering If I'm overthinking thing as I'm thinking the layer 2 path and 3 path need to point to the same root bridge/Layer 3 gateway.
So If I move another customer (move VLAN interfaces) of the RB, do I need to make the new switch RB for the newly configured VLAN interfaces?
Attached 2 pictures of the current situation and the new situation.
Comments
Even in hub-and-spoke environments, I manually set the RB for VLANs on the gateway devices. Also, never disable STP even if it's not used.