Do empty drive bays need to be filled?
It sounds like you bought a repurposed server. The previous owner probably took out their disks and had them destroyed, leaving only empty hot-swap bays.
On new servers those are are filled with either empty drive-trays (and you would place your drive in the tray to populate the slot) or more likely with filler blanks (and the vendor sells you drives ready to use as a single unit already attached to their version of hot swap tray)
Plenty of places sell both filler blanks and drive trays.
As far as I know it is not immediately harmful to leave hot swap bays empty , but it will result in a sub optimal airflow and cooling and you may get some dust build up in any of the exposed connectors which might be something to worry about when you do want to populate those empty slots.
For aesthetics and airflow, fill them. (And blanks usually cost only a couple of $ € £ )
I'm going to add another answer as my other one had information which was incorrect which was my fault for not taking note of the server that you have.
If the server has hot swap bays, then yes, they need to be filled as there would be an open hole in the case. This is also the case for PICe slots that are empty. For example, if you were to remove a NIC, you'd want to put the plate back in place so that hole isn't open. This would even be the case with a workstation
However, some servers have drive bays that are internal whether it's all of them or some of them. Those can be left empty with no problems.
Basically, if the drive bays are hot swappable then they need to be filled. If they are internal then they don't. This is the case whether it's a server or a workstation because what happens is that it can cause problems with airflow and also allow dust to get into the case. Those things aren't the end of the world but they are both something to avoid as they can lead to problems.