"half-installed" means, I think, files physically in place but application not yet configured.
When you uninstalled 2.2.6, it will have removed all the Lazarus components in read-only diskspace but not your local configuration. Is it possible that the new install of 3.0 is trying to update and use that 2.2.6 config ? As I understand it, the answer is 'no' (that happens when you start lazarus) but you are seeing some strange things.
You have not, at any time, run lazarus as root have you ? I sure hope not.
I'd be looking in ~/.lazarus to see if there are any root owned files in there. But a far cleaner and safer approach would be to completely remove ~/.lazarus and try again, perhaps with -
sudo apt install --reinstall lazarus-project
As usual, my real advice is to just install Lazarus from source, Lazarus, by its nature, is not happy up in read-only space. The devs have done a wonderful job of "behind the scenes" stuff to make it appear it is comfortable but it is NOT.
Davo