Upfront, I’m NOT a Rider person, but here are two tips for self-help:
Tip 1
Are you using the internal tools to investigate such things? If not, turn on internal mode, open up Rider and use Tools | Internal Actions | UI Inspector. I didn’t actually need to enable this, it just worked for me when having internal mode turned on.
Now you can Ctrl + Alt + Click on any UI component and get lots of information. So when I go into the Solution view, right-click to open the pop-up, and then press Ctrl+Alt+Click on any action, I can already see lots of info. Sub tip: Hold Alt down and just hover over any element and the UI Inspector will update accordingly.
If you play around with this, you already get some clues. Like on the Edit group, you find that it has a Group SolutionExplorerPopupMenu.Edit.
But why stop there, right?
Tip 2
You do have a Rider installation and things like action groups are usually stored in .xml files. Of course everything is packed in jars, but that doesn’t stop us and you could try a simple guessing game:
You want to know if there is an xml file somewhere that very likely has a filename containing “Rider” and maybe “Actions”. So go into your Rider installation path (you find it in Toolbox | Rider | … | Settings) and open a terminal. We can use find, unzip and grep to check all jars on the fly:
find /path/to/rider -name "*.jar" -exec sh -c 'unzip -l "$1" 2>/dev/null | grep -E ".*Rider.*\.xml$" && echo "=== Found in: $1 ===" ' _ {} \;
And look what you find in lib/modules/intellij.rider.jar:
META-INF/RiderProjectViewActions.xml
You can simply copy and unpack that jar with zip. If you look at the contents, I believe what you were searching for is
<group id="SolutionExplorerPopupMenu">
But even better, now you know how to help yourself.