UTXO Consolidation: Any extra nuance with multisig?

Sending bitcoin to yourself within the same singlesig wallet (or using a coin control tool to select UTXOs) to consolidate UTXOs makes sense to me. I have a stack in singlesig that I was going to consolidate using Sparrow, but its actually an amount that I would feel more comfortable having in a 2-of-3 multisig (a new wallet) for that extra peace of mind. Am I correct that sending to a new wallet will consolidate funds in the same manner as sending/receiving within the same wallet? Any extra nuance with multisig? My thinking is that I'll only move funds to this multisig a handful of times. Appreciate any insights. And Happy Pizza Day!