I haven’t used plain ftp for several years and have had no problems using SFTP with RapidWeaver. In fact if anything it’s much more reliable than ftp and for security I have plain ftp disabled on my host accounts.
Now without more information it’s difficult to say exactly what is causing the issue your having.
You said you host company “moved you” to SFTP server , did they actually change the server? That’d be kinda strange as SFTP is ftp done through a secure shell.
What did you change in publishing settings? Perhaps a screenshot of the publishing settings you are using would help.
What hosting company are you using?
What exact message are you getting when you publish? The “test” button I believe just does a check of basic login credentials.
My first thought would be to check that path. Might be okay but it’s unusual to have a path that starts and ends with the slash /.
Clear out the path entirely
Hit the browse button
If that works you should see a directory list of where the IP address is pointing at. If you see the pubic_html directory(folder) then just select it.
If it doesn’t work then you should get a message (hopefully it’s on the screen long enough) that might help.
As I said earlier the “test” really doesn’t test much other than the credentials so you need to dig a bit deeper.
You might try connecting with a stand-alone ftp client like transmit or FileZilla. They might give you a message that’s a little more help.
Without knowing for sure the hosting company it’s difficult to say if they might have a knowledge base that might help out. Many times host have specific requirements with SFTP such as a port number.
The only other suggestion would be to go through all the steps in this knowledge base article. It’s title is ftp but it still applies to SFTP as it’s ftp over a secure shell. Outlined is how to get a log with more details on the error.