Hey,
I've never changed network profile for iSCSI and Live Migration networks. Public profiles don' have certain services (like file sharing) enabled. It shouldn't have any influence on your issues. https://answers.microsoft.com/en-us/windows/forum/all/should-i-choose-a-public-or-private-network/1544a14f-d7b2-49d4-a26c-26d3b38c5819
What kind of issues are you facing? If you have antivirus software installed, you should check that it doesn't block traffic. You might need to add exclusions to AV software. Might be helpful: https://www.starwindsoftware.com/blog/configure-live-migration-in-hyper-v-clusters
Cheers,
Alex Bykovskyi
StarWind Software
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