Ubuntu: Can't remove ghost default context

Ubuntu 22.04 LTS fresh installation
Installed Docker CE (docker-ce docker-ce-cli containerd.io docker-compose-plugin) and then Docker Desktop (latest 4.22.0). I read that was a mistake, so removed both properly, including sock file and docker folder three in /var/run (installed by Docker CE) and under user $HOME/.
Then I installed again only Docker Desktop, same version.

Surprinsgly, command “docker context ls” still show the context of Docker CE that has been removed.

default moby Current DOCKER_HOST based configuration unix:///var/run/docker.sock
desktop-linux * moby Docker Desktop unix:///home/olivier/.docker/desktop/docker.sock

But command “docker context inspect” does not show it

“Name”: “desktop-linux”,
“Metadata”: {
“Description”: “Docker Desktop”
“Endpoints”: {
“docker”: {
“Host”: “unix:///home//.docker/desktop/docker.sock”,
“SkipTLSVerify”: false
“TLSMaterial”: {},
“Storage”: {
“MetadataPath”: “/home//.docker/contexts/meta/fe9c6bd7a66…”,
“TLSPath”: “/home//.docker/contexts/tls/fe9c6bd7a66301f49ca9…”

Command “docker context show” also only return “desktop-linux”

And when I try to remove the non existing default with command “docker context rm default”, even with the -f flag, it fails with message “default: context “default” cannot be removed”

So looks like there is still a mention of the old default one, but no idea where.
How can I remove it ?

Thanks !