[IMP] website_sale: speed up public category model

Speed up:
- all queries involving `child_of` and `parent_of` by using
	´_parent_store=True` and `parent_path`
- `name_get` by also taking advantage of `parent_path`
- `order by` by indexing the sequence

This reduces the time of the corresponding search lines by 20%.

PR: #34249

addons/website_sale/models/product.py

@@ -139,12 +139,15 @@ class ProductPublicCategory(models.Model):
     _name = "product.public.category"
     _inherit = ["website.seo.metadata", "website.multi.mixin"]
     _description = "Website Product Category"
+    _parent_store = True
     _order = "sequence, name"
 
     name = fields.Char(required=True, translate=True)
     parent_id = fields.Many2one('product.public.category', string='Parent Category', index=True)
+    parent_path = fields.Char(index=True)
     child_id = fields.One2many('product.public.category', 'parent_id', string='Children Categories')
-    sequence = fields.Integer(help="Gives the sequence order when displaying a list of product categories.")
+    parents_and_self = fields.Many2many('product.public.category', compute='_compute_parents_and_self')
+    sequence = fields.Integer(help="Gives the sequence order when displaying a list of product categories.", index=True)
     # NOTE: there is no 'default image', because by default we don't show
     # thumbnails for categories. However if we have a thumbnail for at least one
     # category, then we display a default image on the other, so that the
@@ -178,14 +181,16 @@ class ProductPublicCategory(models.Model):
     def name_get(self):
         res = []
         for category in self:
-            names = [category.name]
-            parent_category = category.parent_id
-            while parent_category:
-                names.append(parent_category.name)
-                parent_category = parent_category.parent_id
-            res.append((category.id, ' / '.join(reversed(names))))
+            res.append((category.id, " / ".join(category.parents_and_self.mapped('name'))))
         return res
 
+    def _compute_parents_and_self(self):
+        for category in self:
+            if category.parent_path:
+                category.parents_and_self = self.env['product.public.category'].browse([int(p) for p in category.parent_path.split('/')[:-1]])
+            else:
+                category.parents_and_self = category
+
 
 class ProductTemplate(models.Model):
     _inherit = ["product.template", "website.seo.metadata", 'website.published.multi.mixin', 'rating.mixin']