Battery Discharging to 1% while connected to power

Make sure you are using the correct size charger for your laptop. A 15" model requires at least an 87W charger while a 16" model requires a 96W charger.

Also make sure the charger is connected directly to the laptop since adapters, dongles, docks, and hubs may not allow the full power of the charger to reach the laptop.

Disconnect all other external devices in case one of them is causing a problem.

Try using the charger on another USB-C port especially on the other side of the laptop in case the USB-C port(s) on the one side are damaged or are partially non-functional.

Try an SMC Reset.

Run the Apple Diagnostics to see if any hardware issues are detected.

Here is an Apple article for troubleshooting USB-C charging issues:

If your USB-C power adapter isn't charging your Mac notebook - Apple Support

You may need to have Apple or an Apple Authorized Service Provider examine the laptop.

Make sure to try the charger in another USB-C port especially on the other side of the laptop if you have the four port model. Also try rotating the USB-C connector of the charging cable 180 degrees upside down (I know it sounds crazy, but the USB-C port may be half bad).

You can monitor the charging and discharging activity using the following command in the Terminal app which will save a copy to a file on your Desktop called "laptop-battery-charge-log.txt". The output will also be displayed in the Terminal window so to terminate the command you need to press Control + C. Maybe it will provide a clue.

pmset  -g  rawlog  |  tee  -a  ~/Desktop/laptop-battery-charge-log.txt

Unfortunately the Apple system logs are now worthless for troubleshooting any issue. Make sure you don't have something that is scheduled to run at night. Maybe your laptop is not actually sleeping. Or maybe you have a corrupt .plist preference file (perhaps "Battery", or "Screensaver", or something else similar that could be related to the old "Energy Saver" preferences or settings for setting timers & usage, etc.) which needs to be deleted and recreated. I'm not familiar with the newer preferences for Big Sur so I cannot be more specific or even tell you where these prefs are located except they should be located in the user's home user Library folder which is hidden by default in the Finder. Or maybe you just found some bug with that version of Big Sur. Make sure Big Sur is completely up to date with the latest patches.

You should also try a clean install by first erasing the whole physical drive before reinstalling macOS and testing the laptop thoroughly before you restore or migrate from a backup and before installing any third party apps. This is the quickest way to figure out if you have a hardware issue and/or a bug with Big Sur. Installing an older version of macOS may be able to determine which of the two is most likely.

As @ku4hx mentions it could easily be a bad battery or even some other hardware issue. I have actually seen an Apple battery stop charging at around 72% on some of the older Magsafe laptops when I'm charging them overnight. That also does not make any sense, but I have seen enough of these laptops do this to know it is not an isolated incident although I'm uncertain whether it indicates a hardware issue or some OS/firmware bug. I have seen some batteries only show a problem when the battery is at a certain charge level.

Something else to consider is whether you are accidentally turning off the electrical power to the laptop either by accidentally turning of the surge strip or the electrical wall outlet. Or maybe you have some other device connected to that electrical circuit that is causing a power issue that is affecting the laptop and this is only occurring at night. This is especially important if you do not live alone as you don't know what someone else may be doing without even realizing it.

I know from personal experience it can be extremely difficult trying to troubleshoot issues with these USB-C Macs.

A charging symbol means absolutely nothing. I have seen a charging symbol, but the battery is not charging. Use the Terminal app command I suggested earlier to log the charging status. It will allow you to see whether the laptop stops charging at some point. Even if the laptop is charging, perhaps it is only very slowly charging which you can tell by how much current is being used. If the laptop is on and running a task when the battery is only slowly being charged, then it is possible for the battery to drain since the laptop will make up for the insufficient power from the charger by pulling power directly from the battery.

Maybe delete the Battery .plist preferences as perhaps the preference file is corrupt.

How old is the battery, i.e. the MacBook? Batteries don't last forever and yours may be at its normal end of life.