Hi there, johnsalter2!
Thanks for using the Apple Support Communities! Based on the information you've given, I understand that when Time Machine is running, your Apple wireless keyboard and Magic Mouse are slow to respond. I use my computer all day, so I know making sure the mouse and keyboard inputs are responding as expected is important, and I have some troubleshooting that should help. Try the following steps (in order), stopping when the issue is resolved.
1. Reset your Mac's System Management Controller. You can read about what the System Management Controller does, and how to reset it, in the article linked below.
Reset the System Management Controller (SMC) on your Mac
Once you've reset the SMC, wait to see if the mouse and keyboard are still slow during the Time Machine backup. If they are, try the next step.
2. Reset the computer's NVRAM. Information on what the NVRAM is and does, as well as how to reset it, can be found in the following article.
How to Reset NVRAM on your Mac
Like the previous step, after resetting the NVRAM test the mouse and keyboard during a backup. If the response is still slower than expected, try the following.
3. Test in safe mode. The article below is will give you more information on safe mode and how to use it. Despite the article's title not being specific to your situation, it is still a relevant step to take because it runs a few checks on the system, and disables certain software that could be causing a conflict.
Try safe mode if your Mac doesn‘t finish starting up
You'll want to test the mouse and keyboard's performance during a backup while in safe mode. Make note of how they perform, then restart the computer as normal and test again. If the issue persists, try the next step.
4. Test in a new user account. Read the article linked below to get more information on how a new user account can help, how to set one up if you need assistance, and what to do if the issue persists beyond this step.
How to test an issue in another user account on your Mac
Have a great day!