Yesterday, at Linda Maryanov's Thursday Think Tank study group, I learned that we can now search for New York Surrogate's Court records online at NYS Courts Electronic Filing (NYSEF). We still cannot search for New York Surrogate's Court records on WebSurrogate.
The screenshot above confirms what I learned. The split-view is of WebSurrogate on the left side and NYSEF on the right side. As you can see, New York County Surrogate's Court is not available as an option from the drop-down menu in WebSurrogate, but it is available as an option on NYSEF.