{% set entries = craft.entries({
  section: 'projects'
}).search('test:testValue') %}

{% set entries = craft.entries({
  section: 'projects'
}).search('entriesfield.id:relatedThemesID') %}

'criteria' => [
  'section' => 'projects',
  'test' => 'testValue'
],

'criteria' => [
    'section' => 'projects',
    'test' => 'testValue'
    'relatedTo' => id
]

'relatedTo' => [
    'sourceElement' => id,
    'field' => 'fieldHandle'
]