"The service 'serializer' has a dependency on a non-existent service 'entity.manager'"
After @leymannx and @Kevin tips I could fix my problem, I will leave step by step what I have done, hope help anyone else :)

Set my sites do Drupal 8 again
Search inside my modules folder if any module use &quot;entity.manager&quot;
Update those modules according module page
Update D8 to D9 with composer
Run update.php (this give couple more errors about compatibility in some modules)
Update those modules

I have a couple of custom modules and custom theme, in those I replace

core: ^8.8

with

core_version_requirement: ^8.8 || ^9

Also have couple more contrib modules with the same problem, so I created a patch for those modules.
After all that could run update.php and everything works as expected.