[IMP] im_livechat, *: Refactor JS Public Livechat (step 16)

*: website_livechat

This commit is a step towards refactoring the JS of public livechat,
so that it reuses the same architecture as the code of Discuss.
This implies code that uses JS models and OWL components.

Task-2965839

closes odoo/odoo#99137

Signed-off-by: Alexandre Kühn (aku) <aku@odoo.com>