PostgreSQL undocumented timenow() function?
Yes, this is undocumented, very old, deprecated for a long time ago stuff.
The key difference from the NOW function is the data type of the result. timenow used the type abstime, which was less accurate and prone to the year 2038 problem. There is a small note in the documentation:

The types abstime and reltime are lower precision types which are used internally. You are discouraged from using these types in applications; these internal types might disappear in a future release.

This type was completely removed in postgresql 12 with all related functions. Per source code I can confirm: yes, timenow will return real time by every call, not the time of transaction start.
You could achieve same result by using clock_timestamp() function instead of now()