Fail to Run Docker After Installation

I’ve installed Docker (Docker Desktop) on my Mac for the first time and I’ve an error running docker after ejecting the installation volume Docker.

I’m using Macbook Pro, M2, MacOS Ventura 13.4.1
I did the GUI installation and completed the installation process. It happens that if I eject the Docker volume (added to the desktop during installation) then docker fails to run - this is what I get when I do:

$ /Applications/Docker.app/Contents/MacOS/com.docker.diagnose check
Starting diagnostics

[PASS] DD0027: is there available disk space on the host?
[PASS] DD0028: is there available VM disk space?
[PASS] DD0018: does the host support virtualization?
[PASS] DD0001: is the application running?
[PASS] DD0017: can a VM be started?
[PASS] DD0016: is the LinuxKit VM running?
[PASS] DD0011: are the LinuxKit services running?
[PASS] DD0004: is the Docker engine running?
[FAIL] DD0015: are the binary symlinks installed? 2 errors occurred:
	* checking binaries in /usr/local/bin: following symlink /usr/local/bin/docker: lstat /Volumes/Docker: no such file or directory
	* checking binaries in $HOME/.docker/bin: unable to find /Users/jack/.docker/bin: stat /Users/jack/.docker/bin: no such file or directory

[PASS] DD0031: does the Docker API work?
[FAIL] DD0013: is the $PATH ok? unable to find docker executable on PATH
[FAIL] DD0003: is the Docker CLI working? exec: "docker": executable file not found in $PATH
[PASS] DD0038: is the connection to Docker working?
[PASS] DD0014: are the backend processes running?
[PASS] DD0007: is the backend responding?
[PASS] DD0008: is the native API responding?
[SKIP] DD0009: is the vpnkit API responding?
[PASS] DD0010: is the Docker API proxy responding?
[SKIP] DD0030: is the image access management authorized?
[PASS] DD0033: does the host have Internet access?
[PASS] DD0018: does the host support virtualization?
[PASS] DD0001: is the application running?
[PASS] DD0017: can a VM be started?
[PASS] DD0016: is the LinuxKit VM running?
[PASS] DD0011: are the LinuxKit services running?
[PASS] DD0004: is the Docker engine running?
[WARN] DD0015: are the binary symlinks installed? 2 errors occurred:
	* checking binaries in /usr/local/bin: following symlink /usr/local/bin/docker: lstat /Volumes/Docker: no such file or directory
	* checking binaries in $HOME/.docker/bin: unable to find /Users/jack/.docker/bin: stat /Users/jack/.docker/bin: no such file or directory

[PASS] DD0031: does the Docker API work?
[PASS] DD0032: do Docker networks overlap with host IPs?

Please note the following 1 warning:
1 : The check: are the binary symlinks installed?
    Produced the following warning: 2 errors occurred:
	* checking binaries in /usr/local/bin: following symlink /usr/local/bin/docker: lstat /Volumes/Docker: no such file or directory
	* checking binaries in $HOME/.docker/bin: unable to find /Users/jack/.docker/bin: stat /Users/jack/.docker/bin: no such file or directory

The symlinks to the docker CLI etc are needed for docker commands to work.

Please investigate the following 2 issues:
1 : The test: are the binary symlinks installed?
    Failed with: 2 errors occurred:
	* checking binaries in /usr/local/bin: following symlink /usr/local/bin/docker: lstat /Volumes/Docker: no such file or directory
	* checking binaries in $HOME/.docker/bin: unable to find /Users/jack/.docker/bin: stat /Users/jack/.docker/bin: no such file or directory

The symlinks to the docker CLI etc are needed for docker commands to work.

2 : The test: is the $PATH ok?
    Failed with: unable to find docker executable on PATH

The directory containing the docker CLI tools must be on the $PATH

But if I mount the installation volume again (just double click on the Docker.dmg file without continuing the installation process at all) everything works fine - running the diagnose check command ends with not errors:

Starting diagnostics

[PASS] DD0027: is there available disk space on the host?
[PASS] DD0028: is there available VM disk space?
[PASS] DD0018: does the host support virtualization?
[PASS] DD0001: is the application running?
[PASS] DD0017: can a VM be started?
[PASS] DD0016: is the LinuxKit VM running?
[PASS] DD0011: are the LinuxKit services running?
[PASS] DD0004: is the Docker engine running?
[PASS] DD0015: are the binary symlinks installed?
[PASS] DD0031: does the Docker API work?
[PASS] DD0013: is the $PATH ok?
[PASS] DD0003: is the Docker CLI working?
[PASS] DD0038: is the connection to Docker working?
[PASS] DD0014: are the backend processes running?
[PASS] DD0007: is the backend responding?
[PASS] DD0008: is the native API responding?
[SKIP] DD0009: is the vpnkit API responding?
[PASS] DD0010: is the Docker API proxy responding?
[SKIP] DD0030: is the image access management authorized?
[PASS] DD0033: does the host have Internet access?
[PASS] DD0018: does the host support virtualization?
[PASS] DD0001: is the application running?
[PASS] DD0017: can a VM be started?
[PASS] DD0016: is the LinuxKit VM running?
[PASS] DD0011: are the LinuxKit services running?
[PASS] DD0004: is the Docker engine running?
[PASS] DD0015: are the binary symlinks installed?
[PASS] DD0031: does the Docker API work?
[PASS] DD0032: do Docker networks overlap with host IPs?
No fatal errors detected.

Any idea what should I do? I tried re-installing, uninstalling, and the manual install procedure as described at Mac | Docker Docs