I had been using Windows 8 and TortoiseSVN icons have been displaying properly, but after installing Windows 10 I can no longer see the icons for the files/folder status.
As others have indicated, the overlay icon registry area is congested. Here is a powershell script that allows you to dump all the overlays in the registry to a file, then after you edit the file to prioritize your overlays the way you want, you can import them back in and protect them against further modifications from other programs running under SYSTEM.
https://github.com/polachz/OverlayIconFix
I had the same problem as OP. Installing version 1.9.2 resolved the issue without any tweak.
TortoiseSVN 1.9.1 will work around the issue by renaming the Overlay Icons (starting with 2 spaces) to make sure they are loaded before the OneDrive icons.
Please upgrade your the Tortoise SVN to the latest one.. I would recommend you to change your Settings see here
Settings -> Icon Overlays -> Status cache
make it as Shell and Apply
Now reboot your machine to reflect the chnages.
I did all of the above and nothing worked. The overlay icons were appearing in Explorer but not in Total Commander.
Eventually what solved the issue for me was that I discovered a command in Total Commander that refreshed the Overlay Icons. To access it, right click on the toolbar and click on "Change...", and add "cm_SwitchOverlayIcons" as shown in the image below.
After adding the command icon to the toolbar, I click it once, and the overlay icon of TortoiseSVN appeared!
You can go to:
Tortoise Settings > Icon Overlays -> Overlay Handlers
and uncheck all checkboxes, apply, then reactivate them and apply.
This will do the same thing in the registry but not manually.
Otherwise you can open the registry with the button below, and move up the keys, appending some spaces before the name.