Can you shed some more light on this "browning out" phenomenon?

Here's the GCP doc [1]. Other live migration products are similar.

Generally, you have worse performance while in the preparing to move state, an actual pause, then worse performance as the move finishes up. Depending on the networking setup, some inbound packets may be lost or delayed.

[1] https://cloud.google.com/compute/docs/instances/live-migrati...