In stage there is project_ids field M2M with project. This is the stages that show in projects's task.

You need to link project in state for link all their tasks.

Below module also usefull for define default stage of each new project-

https://www.odoo.com/apps/modules/12.0/project_task_default_stage/

I have a default field in the project.task.type model to define that the stage is on a new project and normally another many2one field to define the stage usage. 

default_stage = fields.Boolean(string='Stage on new project', default=False)

Then I just extended the project create method to add the default stages to new projects.

@api.model
def create(self, vals):
    ir_values = self.env['ir.values'].get_default('project.config.settings', 'generate_project_alias')
    if ir_values:
         vals['alias_name'] = vals.get('alias_name') or vals.get('name')
         # Prevent double project creation when 'use_tasks' is checked
         self = self.with_context(project_creation_in_progress=True, mail_create_nosubscribe=True)

         default_stages = self.env['project.task.type'].sudo().search([('default_stage', '=', True)])
         stages_list = list()
         for stage in default_stages:
            stages_list.append((4, stage.id))

         if len(stages_list) > 0:
            vals['stage_ids'] = stages_list

         new_project = super(TablaProjectProjectExtension, self).create(vals)
         return new_project 

Try this code please :)

from odoo import models, api, fields, SUPERUSER_ID, _

class ProjectTaskType(models.Model):
	_inherit = 'project.task.type'

	# Step specific code to identify it
	code = fields.Char('Code')

	_sql_constraints = [
		('code_uniq', 'unique (code)', "Stage code already exists!"),
	]

class Project(models.Model):
	_inherit = 'project.project'

	@api.model
	def _read_group_stage_ids(self, stages, domain, order):
		# Call Super Function
		response = super(Task, self)._read_group_stage_ids(stages, domain, order)
		search_domain = [('id', 'in', response.ids)]
		# Append my specifik stages [Stages whose code is equal to todo or inprogress or done or canceled]
		search_domain = ['|', ('code', 'in', ['todo', 'inprogress', 'done', 'canceled'])] + search_domain
		stage_ids = stages._search(search_domain, order=order, access_rights_uid=SUPERUSER_ID)
		return stages.browse(stage_ids)