Option 1:

you can make new many2one computed field and reuse your code, that you posted in the question, inside the compute function for a new many2one field.

.py:

project_id = fields.Many2one(comodel_name="project.project", string="Project", compute="_compute_project_id")

@api.one
def _compute_project_id(self)
    self.project_id = self.env['project.project'].search([('analytic_account_id', '=', self.id)], limit=1) #I simply copied your code here

.xml:

<field name="project_id" />

you can make new one2many field, connecting to the project and in the inverse_name parameter, put the  analytic_account_id, so it'll be automatically find it's other end. It should work, if as you stated the relation is one2one in the practice, and you can then force this field to display as a link, instead of a table, by explicitly putting widget="many2one" in the xml definition of view.

.py:

project_id_s = fields.One2many(comodel_name="project.project", inverse_name="analytic_account_id", string="Project")

.xml:

<field name="project_id_s" widget="many2one" />

There may be more options, but one of the two should work for you I think.