@Zbik

Hello. I tried adding view_id, because everything else I have the same (without target) and still it doesn't work. What I found interesting, is that on one field, my default works just fine. In comment it doesn't.

class InterestNote(models.Model):
    _inherit = 'account.invoice'
    _translate = True

    interest_paid = fields.Boolean(string='Are interests paid?', help='Boolean to see if interests are already paid.',
                                   default=False)
    # tester = fields.Text(string='TEST', default=get_comment_test)

    @api.multi
    def interest_note(self):
        _logger.info(f'ID FAKTURY: {self.id}')
        _logger.info(f'NUMER FAKTURY: {self.number}')
        _logger.info(f'PARTNER: {self.partner_id}')
        _logger.info(f'COMMENT: {self.comment}')
        _logger.info(f'COMMENT TYP: {type(self.comment)}')
        com = self.comment
        # ctx = dict(
        #     type='out_invoice',
        #     comment=com
        # )
        _logger.info(f'COM: {com}')
        _logger.info(f'COM TYPE: {type(com)}')

        # inv_obj = self.env['account.invoice']
        # inv = inv_obj.create(ctx)
        # _logger.info(f'ID FAKTURY INV: {inv.id}')
        # return {'type': 'ir.actions.act_window_close'}

        return {
            'name': 'Create new interest note',
            'type': 'ir.actions.act_window',
            'view_type': 'form',
            'view_mode': 'form',
            'view_id': self.env.ref('account.invoice_form').id,
            'res_model': 'account.invoice',
            'context': {
                'type': 'out_invoice',
                'default_type': 'out_invoice',
                'comment': com,
                'default_comment': com
            },
            'target': 'current'
        }

    @api.model
    def get_comment_test(self):
        _logger.info('FUNKCJA TEST ROZPOCZYNA SIĘ')
        test_com = self.env.context.get('comment')
        _logger.info(f'TEST COM: {test_com}')
        _logger.info(f'TEST COM TYPE: {type(test_com)}')

        if not test_com:
            test_com = '456'

        return test_com

    comment = fields.Text('Additional Information', default=get_comment_test,
                          readonly=True, states={'draft': [('readonly', False)]})
    tester = fields.Text(string='TEST', default=get_comment_test)

Field comment is still without any values when new invoice, but field tester works. Why is that? It's so confusing right now, I really do not understand why in one field something works, but in another it doesn't.

Your problem is probably related to something else.
In module sele field comment is redefined too.
See:
def _default_comment(self):
invoice_type = self.env.context.get('type', 'out_invoice')
if invoice_type == 'out_invoice' and self.env['ir.config_parameter'].sudo().get_param('sale.use_sale_note'):
return self.env.user.company_id.sale_note

comment = fields.Text(default=_default_comment)

If your module not depends on sale then result in this field may be different than you expect .

PS. It is easier to use (if sale not inherit, without redefinition the commment field):  

return {
  'name': 'Create new interest note',
  'type': 'ir.actions.act_window',
  'view_type': 'form',
  'view_mode': 'form',
  'view_id': self.env.ref('account.invoice_form').id,
  'res_model': 'account.invoice',
  'context': {'type':'out_invoice', 'default_type': 'out_invoice', 'default_comment': com },
  'target': 'new'
}