Make data types into plugins

Also possibly worth a thought: introduce a proper method for checking for data type support in a service class, instead of using a "magic name" supportsFeature() call.

Great work, Mattias, thanks!
I didn't try it out yet, but I looked over the code and saw only a few minor issues:

1. +++ b/search_api.services.yml
   @@ -18,3 +18,7 @@ services:
        arguments: ['@database', '@entity.manager']
   +
   +  plugin.manager.search_api.datatype:
   +    class: Drupal\search_api\Datatype\DatatypePluginManager
   +    parent: default_plugin_manager
   

   Unless I'm mistaken, services should generally be sorted alphabetically, so this should go further up.

2. +++ b/src/Datatype/DatatypeInterface.php
   @@ -0,0 +1,43 @@
   + * Contains \Drupal\search_api\Datatype\DatatypeInterface.
   

   In my eyes, this looks weird, I'd prefer DataType for both namespace and class names. It's the same in method names already, after all.
   Of course, we use "datasource" as one word, but I think that's a special case.

3. +++ b/src/Datatype/DatatypeInterface.php
   @@ -0,0 +1,43 @@
   +  /**
   +   * Converts a value .
   +   *
   +   * @param mixed $value
   +   *   The value to convert.
   +   *
   +   * @return mixed
   +   *   The converted value.
   +   */
   +  public function getValue($value);
   

   Incomplete doc comment.

4. +++ b/src/Datatype/DatatypeInterface.php
   @@ -0,0 +1,43 @@
   +  /**
   +   * Returns the fallback default datatype for this datatype.
   +   *
   +   * @see \Drupal\search_api\Utility::getDefaultDataTypes()
   +   *
   +   * @return string
   +   *   The fallback default datatype.
   +   */
   

   @see should come after @return. See the documentation standards.

5. +++ b/src/Datatype/DatatypePluginBase.php
   @@ -0,0 +1,53 @@
   +namespace Drupal\search_api\Datatype;
   +use Drupal\search_api\Plugin\IndexPluginBase;
   

   These should be separated by an empty line.

6. +++ b/src/Datatype/DatatypePluginBase.php
   @@ -0,0 +1,53 @@
   +}
   \ No newline at end of file
   

   Missing trailing newline.

7. +++ b/src/Utility.php
   @@ -80,46 +77,97 @@ class Utility {
   +   *   A nested associative array with the default types as keys, mapped to their
   

   Overlong comment line.

8. +++ b/src/Utility.php
   @@ -80,46 +77,97 @@ class Utility {
   +        'label' => \Drupal::translation()->translate('Fulltext'),
   

   I think just using the t() function is fine here, too. You should only use the OOP way if you can inject the translation manager.

9. +++ b/src/Utility.php
   @@ -80,46 +77,97 @@ class Utility {
   +   * @return string[]|null
   +   *   If $type was not given, an array containing all data types, in the
   +   *   .
   

   Incomplete doc comment.

Thanks, great work, looks very good already!
Just had a few code style fixes, in the attached patch. Please reviw to see if you agree with them. (The empty line before the end of a class is my personal taste, but currently (I think) uniform within the module.)
Also, it seems this is still missing the page listing all data types? Or is there already an issue for that?

Great, committed.
Thanks again!