Lag in typing after battery replacement on MacBook Pro

See if something is using significant compute resources:

Activity Monitor User Guide for Mac - Apple Support

If you restored the machine from a backup, Spotlight will spend a few hours/days (depending on data quantity) indexing it and that can slow down the system.

<lsd Crash (6 times)>

lsd is a process that stands for LaunchServiceDaemon. This daemon plays a critical role in managing and launching applications, associating document types with specific apps, and defining the execution environment for bundled code.

I might suspect these as possibilities...

<inkscape Crash>

< ProtonVPN>

<steamclean >

< cleverfiles>

<Raycast>

Uninstall all third party apps that are Cleaners/Optimizers/VPN/Anti-Virus

all known to cause issues on the macOS

unplug all non-essential peripherals when testing

To trouble shoot further you can:

—A SafeBoot Start up your Mac in safe mode - Apple Support will sort many anomalies

Does a quick disk repair before it fully boots up, and certain system caches get cleared and rebuilt, third party system modifications and system accelerations are disabled temporarily.

Login and test. Reboot as normal and test. Caches get rebuilt automatically.

This test will tell you if third party interference; most extensions etc are not loaded in safe boot mode.

—Test issue in another user (or guest user) account Change Users & Groups settings on Mac - Apple Support

This will tell you if it a universal issue or isolated to your user/admin account. 

***wireless keyboard with rechargeable batteries— connect the charging cable, this will make the wired keyboard successful Safe Boot your Mac.