Solr default search indexes exception: IDocumentBuilderOptions of wrong type for this crawler

Question

We are in the process of upgrading from Sitecore 10.0.1 to Sitecore 10.3. We used Azure search which is no longer supported. Following the installation process, and setting up the default indexes sitecore_master_index, sitecore_web_index and sitecore_core_index, not all documents are indexed as expected.

After a rebuild of the indexes, the document count is as follows (and the values of 10.0.1 environment next to it):

• core: 0 documents (10813 documents)
• web: 7174 documents (24022 documents)
• master: 22096 documents (25366 documents)

So it is expected that core is filled with ~10.000 and web and master should be approximately equal. Looking in the sitecore logging, the following exceptions appear for items in both web and core:

ManagedPoolThread #8 12:11:54 WARN  [Index=sitecore_core_index] Crawler : AddRecursive DoItemAdd failed - {11111111-1111-1111-1111-111111111111}
Exception: Sitecore.Exceptions.RequiredObjectIsNullException
Message: IDocumentBuilderOptions of wrong type for this crawler
Source: Sitecore.ContentSearch.SolrProvider
   at Sitecore.ContentSearch.SolrProvider.SolrIndexOperations.IndexVersion(IIndexable indexable, IProviderUpdateContext context)
   at Sitecore.ContentSearch.SolrProvider.SolrIndexOperations.ApplyPermissionsThenIndex(IProviderUpdateContext context, IIndexable version)
   at Sitecore.ContentSearch.SitecoreItemCrawler.DoAdd(IProviderUpdateContext context, SitecoreIndexableItem indexable)
   at Sitecore.ContentSearch.HierarchicalDataCrawler`1.CrawlItem(T indexable, IProviderUpdateContext context, CrawlState`1 crawlState) 

What does this exception mean? And how can we get the indexes working? The files in \App_Config\Sitecore\ContentSearch (Sitecore.ContentSearch.Solr.Index.Web.config, Sitecore.ContentSearch.Solr.Index.Core.config, Sitecore.ContentSearch.Solr.DefaultIndexConfiguration.config, ...) are not adjusted and contain the default configurations

Update

The sitecore_core_index definition in /sitecore/admin/showconfig.aspx is as follows:

<index id="sitecore_core_index" type="Sitecore.ContentSearch.SolrProvider.SolrSearchIndex, Sitecore.ContentSearch.SolrProvider">
    <param desc="name">$(id)</param>
    <param desc="core">sitecore_core_index</param>
    <param ref="contentSearch/indexConfigurations/databasePropertyStore" desc="propertyStore" param1="$(id)"/>
    <configuration ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration"/>
    <strategies hint="list:AddStrategy">
        <strategy ref="contentSearch/indexConfigurations/indexUpdateStrategies/intervalAsyncCore"/>
    </strategies>
    <locations hint="list:AddCrawler">
        <crawler type="Sitecore.ContentSearch.SitecoreItemCrawler, Sitecore.ContentSearch">
            <Database>core</Database>
            <Root>/sitecore</Root>
        </crawler>
    </locations>
</index>