Jetbrains Datagrip icon cannot lock to the launcher
Use the command described by @JonasCz. "Tools" > "Create desktop entry / launcher"
Then go to unity, search for DataGrip and drag it to the bar.
I don't know why pinning it doesn't work but the above worked for me. I imagine it has to do with pining the shortcut vs the running java app. The shortcut is probably a wrapper to start the main app.