Refresh mechanism doesn't launch the latest installer version

[d-loose]

What happened?

After updating the installer and restarting it through its refresh page, the version that was shipped on the iso is launched again.

What was expected?

The latest version installed by the update should have been launched.

Steps to reproduce

1. Start a live session from an iso with an outdated installer version
2. Click on 'update to version ...' on the refresh page
3. Click 'restart'

Additional context

Before updating:

$ snap info ubuntu-desktop-installer
name:      ubuntu-desktop-installer
summary:   Ubuntu Desktop Installer
publisher: Canonical**
store-url: https://snapcraft.io/ubuntu-desktop-installer
contact:   https://bugs.launchpad.net/ubuntu-desktop-installer/+filebug
license:   unset
description: |
  This project is a modern implementation of the Ubuntu Desktop installer,
  using subiquity as a backend and Flutter for the UI.
commands:
  - ubuntu-desktop-installer.os-prober
  - ubuntu-desktop-installer.probert
  - ubuntu-desktop-installer.subiquity-loadkeys
  - ubuntu-desktop-installer
services:
  ubuntu-desktop-installer.subiquity-server: simple, enabled, active
snap-id:      rQm0TtMOYOtEslvEXgxQDhgy1JNn38Wz
tracking:     latest/stable/ubuntu-23.10
refresh-date: 6 days ago, at 02:30 UTC
channels:
  latest/stable:    0+git.1c719695 2023-10-16 (1269) 137MB classic
  latest/candidate: 0+git.1c719695 2023-10-16 (1269) 137MB classic
  latest/beta:      ^                                      
  latest/edge:      ^                                      
installed:          0+git.bca6e31c            (1257) 137MB classic

ubuntu@ubuntu:~$ pgrep -alf installer
1812 /bin/bash /snap/ubuntu-desktop-installer/1257/bin/subiquity-server
1826 /snap/ubuntu-desktop-installer/1257/usr/bin/python3.10 -m subiquity.cmd.server --use-os-prober --storage-version=2 --postinst-hooks-dir=/snap/ubuntu-desktop-installer/1257/etc/subiquity/postinst.d
2851 /bin/bash /snap/ubuntu-desktop-installer/1257/bin/launcher /snap/ubuntu-desktop-installer/1257/bin/ubuntu_desktop_installer --try-or-install
2945 /snap/ubuntu-desktop-installer/1257/bin/ubuntu_desktop_installer --try-or-install

After updating:

ubuntu@ubuntu:~$ snap info ubuntu-desktop-installer
name:      ubuntu-desktop-installer
summary:   Ubuntu Desktop Installer
publisher: Canonical**
store-url: https://snapcraft.io/ubuntu-desktop-installer
contact:   https://bugs.launchpad.net/ubuntu-desktop-installer
license:   unset
description: |
  This project is a modern implementation of the Ubuntu Desktop installer,
  using subiquity as a backend and Flutter for the UI.
commands:
  - ubuntu-desktop-installer.os-prober
  - ubuntu-desktop-installer.probert
  - ubuntu-desktop-installer.subiquity-loadkeys
  - ubuntu-desktop-installer
services:
  ubuntu-desktop-installer.subiquity-server: simple, enabled, active
snap-id:      rQm0TtMOYOtEslvEXgxQDhgy1JNn38Wz
tracking:     latest/stable/ubuntu-23.10
refresh-date: today at 09:30 UTC
channels:
  latest/stable:    0+git.1c719695 2023-10-16 (1269) 137MB classic
  latest/candidate: 0+git.1c719695 2023-10-16 (1269) 137MB classic
  latest/beta:      ^                                      
  latest/edge:      ^                                      
installed:          0+git.1c719695            (1269) 137MB classic

ubuntu@ubuntu:~$ pgrep -alf installer
2851 /bin/bash /snap/ubuntu-desktop-installer/1257/bin/launcher /snap/ubuntu-desktop-installer/1257/bin/ubuntu_desktop_installer --try-or-install
4443 /bin/bash /snap/ubuntu-desktop-installer/1269/bin/subiquity-server
4456 /snap/ubuntu-desktop-installer/1269/usr/bin/python3.10 -m subiquity.cmd.server --use-os-prober --storage-version=2 --postinst-hooks-dir=/snap/ubuntu-desktop-installer/1269/etc/subiquity/postinst.d

Note that the frontend is still using the old revision.