Error codes 119 and/or 120 loading existing saves, or 100 starting a new game

Error codes 119 and (the sometimes related) 120 are load errors copying files and initializing the level cache. These can also be associated with error code 100, a problem loading the initial level cache. Generally these error codes are related to My Documents problems.

One person with 119/120 errors in D:OS EE found that the problem was due to their My Documents folder being located on a NAS device, and the NAS being temporarily unavailable. Another had a hard drive removed and Windows showed the correct new location for My Documents in Explorer, but the registry still listed the path on the non-existent drive.
Another person was a little too aggressive freeing up drive space and somehow disabled the ability to create folders in My Documents; a system restore fix that.
A few people with D:OS Classic got these errors after upgrading to Windows 10, due to changes in how Windows handled file permissions (running the game as administrator or adding the current user to the folder permissions would fix the problem in that case).

Try shutting down all non-essential programs (especially anti-virus) before starting the game.
A couple of people have had BitDefender falsely flag the game as ransomware, and block it from creating files and folders. In that case, including both the game executable and Larian Studios My Documents folder in BitDefender's trusted app and directory sections should fix the problem (Advance Threat Defense, Ransomware Protection / Safe Files, Application Access).
Backup and sync programs that monitor the My Documents folder have also caused problem with saving and loading, if they lock the saves or files in the LevelCache folder.

Try exiting out of the Steam client, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file, by right clicking and running as administrator.
If that helps, you can right click the executable file again, select Properties, switch to the Compatibility tab, and check off the option to always run as administrator.

Try creating a new Windows administrator user account, either leaving the My Documents folder in the default location or trying a different drive (if available), switch to that account, and then start the game directly from the executable.
If that lets you load and create profiles, and save and load properly after restarting the game, that would indicate the issue is probably related to the My Documents in the other profile (that was what prompted the person with the registry error to check there).

Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Files...' button.
With the GOG version, in the (optional) Galaxy client, select the game, then the settings icon at the top right (beside the Play button) and under Manage Installation select 'Verify / Repair'.

If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Alternately, exit out of the Steam client, or Galaxy for GOG, and just start the game directly from the executable when required.

Next, try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing. With Steam / Galaxy running and cloud support enabled, the client would just download the cloud copy of your existing profile.
After that, start D:OS 2 DE, create a new profile and see if you can start a new game and save/load. Exit and then copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that lets you load the saves, move the rest of the saves over.
If a new profile doesn't help, delete the new My Documents D:OS 2 folder and rename the original back again.