With a vanilla (unenchanted) fishing rod, pressing the use (right click) waves rod but does not cast.  I have tested this in both single player (on Windows 10) and server (on Ubuntu with client on Windows 10) and in both 21w11a and 21w13a.  Single clicks don't cast, but once, while standing at the water's edge and holding right-click, I caught a fish but saw no casting or bobber.