It's not possible to inherit function from Old Api to New Api

If you want change the method called for a compute field. In the first time you should inherit of the model. And in this model you override the function field with your function

Old api

class account_account_type(osv.osv):
    _name = "account.account.type"
    _description = "Account Type"

     ....

    def _get_current_report_type(self, cr, uid, ids, name, arg, context=None):
        res = {}
        financial_report_ref = self._get_financial_report_ref(cr, uid, context=context)
        for record in self.browse(cr, uid, ids, context=context):
            res[record.id] = 'none'
            for key, financial_report in financial_report_ref.items():
                list_ids = [x.id for x in financial_report.account_type_ids]
                if record.id in list_ids:
                    res[record.id] = key
         return res  
     .... 
    _columns = {
 'name': fields.char('Account Type', required=True, translate=True),
      ......
 'report_type': fields.function(_get_current_report_type, fnct_inv=_save_report_type, type='selection', string='P&L / BS Category', store=True,
            selection= [('none','/'),
                        ('income', _('Profit & Loss (Income account)')),
                        ('expense', _('Profit & Loss (Expense account)')),
                        ('asset', _('Balance Sheet (Asset account)')),
                        ('liability', _('Balance Sheet (Liability account)'))], help="This field is used to generate legal reports: profit and loss, balance sheet.", required=True),
        'note': fields.text('Description'),
    }

New api

Class account_account_type(models.Model):
    _inherit = "account.account.type"
    _description = "Account Type inherited"

     ....
   
 @api.depends('field1')
 def _your_function(self):
     Your code here        
     .... 


    report_type': fields.Selection(compute='_your_function',string='Report' ....