In the website settings, one of the fields allows you to switch settings
from one website to another. Unfortunately, as soon as the user did this
the record was considered to have changed (dirty) and therefore required
a save when it wasn't necessary. The previous commit prevents the header
settings (like the website switcher) from dirtying the record. This was
really necessary because as soon as a user had several websites, it was
impossible for him to access certain settings on all these websites
(except the first one). As soon as the setting performed an action, a
save was required (because the record was dirty) and the user was
redirected to the settings again.
Steps to reproduce the issue before the previous commit:

Install website
Have multiple websites
Go to Settings > Website Settings
Change the website
=> The user is notified that the record has changed and needs to be
saved, which is not true. So far it's annoying but not critical, but if
the user continues:

Activate the "Extra step during checkout" option
Click on "Configure Form"
=> The Save/Discard dialog appears because the record is dirty.

Click on "Save"
=> The user is redirected to the settings page again and cannot access
the form configuration of the second website. (it is the same issue for
most of actions).

The previous commit fixes the issue and this commit adds a test to
ensure that the users are able to change settings of multiple websites.

task-3265100

closes odoo/odoo#125550

Signed-off-by: Aaron Bohy (aab) <aab@odoo.com>