Using this example, there is a setup for build.publish with a value of public. There is no build really just a nice simple index.hml file in the public path. Using a netlify.yml file for the config, but a netlify.toml had the same issue.
See this Deploy log and the image below. The deploy is from the root.

Thanks for the report @talves I've reproduced the issue over here.
To get this working, the temporary "fix" is setting the publish directory in the UI for this site

This should be resolved soon!
I left the publish directory empty on purpose to test. Also, it was interesting the publish directory would normally fill based on the values in the .toml or that is what I thought was the process when creating a new site and picking the github repo. Glad you were able to reproduce.
@talves there have been some progress on issues related to this problem. Could you confirm whether this issue is now fixed? Thanks!
@ehmicky It doesn’t seem to work for me. Please see the build log for “Starting to deploy site from ''” and the corresponding netlify.toml file.
Seems to be the same @ehmicky as before. You can test against this repo https://github.com/talves/netlify-plugin-debug
@kripod @talves I just looked into it and you're correct. I think I've identified the issue. I will post once we have more information.
@kripod @talves This should be fixed now.
I have tested against talves/netlify-plugin-debug and it correctly deploys.
Thanks for your patience and please let me know if there is anything else that is still broken.
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@kripod @talves I just looked into it and you're correct. I think I've identified the issue. I will post once we have more information.