Recently the Federal Reserve raised interest rates by 0.25%. It seems to me that in the modern era there is no reason to pick a round number like 0.25%. It also seems to me that they could / should fine tune interest rates by increasing them a little bit every week. Say by 0.05%. I understand in the past, that you could not have have 14 way calling but those days are gone. For example, we have Zoom and Skype.
The federal funds rate is the interest rate that banks charge each other to borrow or lend excess reserves overnight. The Fed sets a range for this band (typically 0.25% wide) and the rate itself (called Fed Funds Effective rate) is allowed to float freely within the boundaries of the band.
The use of the discount window was discouraged by the Fed itself until around 2003. Even in the financial crisis of 2008, banks were reluctant to borrow at the Fed due to the stigma associated with this. The rate is higher than interbank, and a bank frequently only uses it as a last resort. There is little use of this rate in normal times. For this reason, it should not make a noticable difference if the Fed were to change the discount window frequently or set it at odd levels.