Well, I think, we figured it out. Added the follwing lines to managed-schema:
<field name="tag" type="text_general" indexed="true" stored="true" multiValued="true" />
…
<copyField source="property.XWiki.TagClass.tags_string" dest="tag"/>
and adjusted the page SolrSearchConfig in XWiki to use this new field with an appropriate weight:
'queryFields': { 'DOCUMENT': 'title^10.0 name^10.0 tag^5 …
The query in the correspondig tag source in Search Suggest in the XWiki admin section must be set, accordingly, to:
fq=type:DOCUMENT
qf=tag
Now the search for tags is case-insensitive.