Xbox Series X Controller cursor lag after update.

On Xbox Series X when some games like Doom Eternal, Crash Bandicoot 4, Psychonauts 2, Tales of Arise and Visage are launched (only Xbox Series X enhanced games and not all of them) any Xbox Series X controller incur in an input issue, with battery and with USB cable without battery: if any key or trigger is pressed rapidly it doesn't work, a sort of input lag. The issue persist in any dashboard menu, then if I turn off and turn on the controller again the problem disappear until I return to the game in background that caused the issue. Any Xbox One X controller works perfectly instead. Both Xbox Series X and Xbox Series X controller are update with the latest update. I noticed that when the issue start the usual buzzing noise of the controller change sound, a lower sound. If I plug any headphone with or without microphone in the Xbox Series X controller the commands are more responsive but the problem remains. I reported more and more times this problem to Microsoft since 3 months but still there isn't an update that resolve this issue with my great disappointment. I think this issue started since about 4 months after a system update, and I think the problem is the same of yours. Can you confirm this?

I have an issue similar to yours and identical to other users: even after OS update 10.0.22000.2656,
on Xbox Series X when some games like Doom Eternal, Crash Bandicoot 4, Psychonauts 2, Tales of Arise and Visage are launched (only Xbox Series X enhanced games and not all of them) any Xbox Series X controller incur in an input issue, with battery and with USB cable without battery: if any key or trigger is pressed rapidly it doesn't work, a sort of input lag. The issue persist in any dashboard menu or in any other game that don't give this issue, then if I turn off and turn on the controller again the problem disappear until I return to the game in background that caused the issue. Any Xbox One X controller works perfectly instead. Both Xbox Series X and Xbox Series X controller are update with the latest update. I noticed that when the issue start the usual buzzing noise of the controller change sound, a lower sound. This issue started since about 4 months after a system update. I have reported many times this issue and it has been reported by other users too.
Analog sticks and triggers calibration from the system menu is missing, an essential feature in my opinion, I'm reporting this since 3 years.

In this case, it wouldn't be a bad idea to update your controller's firmware. You can do this on your Series X or your Windows 10 PC. To do it on the Series X, connect it using the USB cable and then go to Settings > Devices & connections > Accessories, and then select the controller you want to update. On the Xbox Wireless Controller screen, select “…” to check the firmware version for your controller. Then, select the Firmware version square, and then press Next to start the update process.

To do it on Windows 10, just download the Xbox Accessories app from the Microsoft Store. If you already have it installed, just run it. After opening the app, the procedure to update is the same one as on the Series X, press the "..." button and follow those steps.

Check if your controller works correctly after doing this.

Thanks Jason for you’re answer !

But when i move my cursor by Microsoft, it jerks. I don’t think its the Game compatibility.

What’s the polling rate of the mouse on Xbox Serie X ?

What’s the delay to the answer of the keyboard and after the mouse ?

Given it started after a firmware update, then it's likely the update caused it...sometimes updates have unintended consequences and it's possible that it has disrupted the ability to use the new Series X/S controllers on older XBox One systems. If that's the case, they will hopefully fix it with another update, though it may be a while