On servers that I run, InhabitedTime does not appear to affect the Local Difficulty in the Debug (F3) menu. May be a visual glitch, but I can't be sure really.

First, to make sure my method works, I'll try doing it on a Singleplayer world:

1. Create a Singleplayer world, in Hard difficulty. Creative mode for flying just in case, has no effect on Local Difficulty.
2. Enter the Singleplayer world, so you load some chunks into the world's save file.
3. Use the Debug menu to find what chunk you spawned in.
4. Exit the Minecraft world, so that you can edit the world file.
5. Open the Minecraft world's save folder using an NBT editing software (i'm using NBTExplorer)
6. Find the chunk you were positioned in, in a "WORLDFOLDER/region/r.x.z.mca" file
7. In the folder for that chunk, change the "InhabitedTime" stat to 3,600,000. This is the maximum effect for InhabitedTime on Local Difficulty. Make sure to save the change!
8. Re-enter the Singleplayer Minecraft world. If you edited the InhabitedTime of the right chunk, on Day 0 (full moon), the Local Difficulty will be 5.25. If you edited the wrong chunk, search around for it, or try again to find the right chunk to edit.

Doing it in Singleplayer, it works just as expected. After spending 3,600,000 ticks (50 hrs) with a chunk loaded will increase the difficulty by 3, in Hard mode.

Let's test this again with the same steps, except using a Multiplayer server.

1. Get server software from minecraft.net, if you don't have it. Preferably store it in a new, seperate folder, to avoid clutter.
2. Run the server.jar file, then go in the eula.txt file to set it to true, and save.
3. Run the server.jar file again, to initialize the server.
4. After the server finishes loading, enter the server using a vanilla 1.16.1 Minecraft Client, so you can load some chunks in.
5. Use the Debug menu to find what chunk you spawned in, just like the Singleplayer world.
6. Exit the Minecraft world on the client, and close the Minecraft Server.
7. Open the server's Minecraft world save folder, again using an NBT editing software.
8. Find the chunk you were in, in a "SERVERFOLDER/world/region/r.x.z.mca" file
9. Edit the "InhabitedTime" for that chunk to 3,600,000, and save the change.
10. Re-open the server.jar file to start up the server again, then re-enter the server from the Minecraft client.
11. To make sure the numbers are consistent with our server, enter the server's console and make the world Hard difficulty by entering "/difficulty hard". Also change yourself to Creative mode if you need to.
12. Check the Debug menu on the client, while on the chunk that you edited the InhabitedTime for. Currently, with Day 0 (full moon), in the chunk I edited (triple checked), and following these steps, InhabitedTime has no effect on the Debug menu, and reads 2.25 rather than 5.25

Again, I'm not sure if this is visual or the server doesnt even account for InhabitedTime. Maybe the server doesnt update the client on InhabitedTime, and the client keeps it at 0, while the server continues to update Local Difficulty on its side, according to InhabitedTime.

Whichever it is, something clearly isn't adding up.