I don't know how similar it is, but KDE's Dolphin file manager has git integration, I don't know how similar it is to TortoiseGit, it might be worth checking out

https://apps.kde.org/dolphin_plugins/

This is something I have not heard before. Can you please explain your use case a bit more?

What commands do you run using right click? Do you strongly prefer this over a terminal window? You can have aliases if you'd like.

I do virtually everything through tortoisegit, and much prefer it over a CLI. When you right click, you get this:

https://i.postimg.cc/hG4g8pjp/tgit.png

Which gives you basically everything you could ever possibly want. My main use cases for it vs a terminal interface are:

1. When you commit, you get this:

https://i.postimg.cc/90YJBtz1/boaty.png

Clicking the files brings up a diff, which makes pre commit reviews extremely easy. Its a lot faster to add files via an interface like this, rather than using a cli

2. The graphical log feature is pretty indispensable for complex projects. Eg check out this:

https://i.postimg.cc/qRb76Wxj/godot-mergy.png

This is much nicer than trying to do grok this through the cli for me. Reverting commits, cherrypicking, merges, splicing the history, seeing all the available branches, keeping track of orphaned commits etc, is all super easy

3. If I have to pick between not remembering the CLI commands off the top of my head, and having to memorise and alias a whole bunch of commands to be able to use git fully, I'll pick the former every day. Its the same reason I use an IDE

I wouldn't object to it being a standalone tool, but the nice thing about it being on the context menu is that it doesn't intrude when you don't need it

Any modern IDE has those functionalities, and most of them run on Linux too. I don't think there is anything you have shown that warrants sticking to Tortoise Git instead of any other IDE.

Also if you don't want to use an IDE Gnome's file manager nautilus supports scripts available on right click. This would allows you to run git commands from the file manager , show the information you need using [YAD](https://yad-guide.ingk.se/#_introduction)

Tortoisegit isn't an ide though, and the quality of git integration varies wildly between different ides - many of them have pretty toy integration. Its much nicer to have proper quality support of uniform quality, rather than having to rely on whatever you happen to be using at the time

Ideally I'd like to avoid having to reimplement the whole thing from scratch using ad-hoc scripts

There seem to be some git tools on Linux that integrate with some filemanagers e.g. https://flathub.org/en/apps/de.philippun1.turtle

I stand boggled.

Try git cola.