Adjustments for nested documents usage

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Setup

• Solr version: 9.6.1
• Drupal Core version: 11.2.1
• Search API version: 8.x-1.38
• Search API Solr version: 4.3.10
• Configured Solr Connector: Standard

Issue

This is a follow up of old issue with nested documents. Since that issue was raised I believe a lot was changed and it is not possible just to use the "String" type for a field in the processor anymore, because the object can't be converted to the string. Therefore some small adjustments are needed to the code to be able to actually put nested documents to Solr index.

PR will contain those adjustments.