Before doing anything else make sure you have a good backup now while you still can. People should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. There are a lot of new ways to permanently lose access to the data on the internal SSD with the recent Macs due to all the hardware, software, and security changes.
This is most likely a hardware issue of some sort which will require a hardware repair since you are seeing several different types of graphical anomalies. Have Apple or an Apple Authorized Service Provider examine the laptop to confirm.
Disconnect all external devices from the laptop in case one of them is causing a problem.
Try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics rarely detect problems, but it never hurts to try. If you see graphical glitches while running the diagnostics or while booting to the diagnostics, then it is a good indicator of a hardware issue even if the diagnostics pass, although I have seen some graphical glitches that may be normal (seeing a red box around the Apple or the progress bar, or seeing "snow" on the screen as the video changes to another mode...should only occur once).
You can try the following to confirm as well:
Boot into Recovery Mode and launch the Terminal app from the Utilities menu on the menu bar. If the macOS installer launched automatically, then just quit the installer app to access the main recovery mode screen. Issue the following command in the Terminal app which will clear out the NVRAM which contains some configuration & boot settings. This is safe to use on both Intel & M-series Macs (you may see a permissions issue about not being able to delete the computer name and some other similar items which is Ok):
nvram -c
One option would be to boot into Safe Mode to see if the problem still occurs. If Safe Mode works, then most likely you have an issue with some third party software that is installed.
If you have at least 80GB+ of Free storage space on the internal SSD (ignore the "Available" space designation as it is misleading), then you can create a new APFS volume on it (give it a unique name). Then you can install a fresh copy of macOS onto the new APFS volume. Boot into the new OS on the new APFS volume to see if you have the same graphical glitches. Do not restore from a backup, do not install any third party apps, and do not sign into your AppleID or iCloud. You must test the system using a pristine copy of macOS. If you have no issues with this, then you most likely have a software or configuration issue with the original OS installation. Before deleting the new APFS volume, make sure to reselect the default Startup Disk in System Settings & reboot to the original OS so that you don't encounter any boot issues. This option allows you test a fresh copy of macOS without interfering with the original macOS installation or data, but it is not a 100% definitive confirmation test if you still encounter issues.
You can try performing a DFU firmware Revive which resets the security enclave & system firmware. This should leave your current macOS & data intact. You should make sure you have a good backup just to be safe since it is possible you could lose access to the data on the internal SSD if the process does not complete successfully.
The best way is by performing a DFU firmware Restore which resets the security enclave chip & system firmware as well as pushing a clean copy of macOS to the internal SSD. This destroys all existing data on the internal SSD & is the best test. Just make sure to thoroughly test the laptop before restoring from a backup, before installing any third party software, and before signing into your AppleID or iCloud. If you still have the issue under these conditions, then you have confirmed a hardware issue.
However, if you don't have access to another Mac that can perform a DFU firmware Revive or Restore, then you could also perform a clean install of macOS by first erasing the disk followed by reinstalling macOS. Again, make sure to thoroughly test the laptop before restoring from a backup, before installing any apps, and before signing into your AppleID or iCloud. This option is not quite as thorough as the DFU firmware Restore, but it is very close.