Especially what is in the "fts" header vs. "next uid" header? Does the UID in "fts" header keep changing every time you save a new mail? I suppose it will.

Diff between 2 emails:
next uid = 30104 | next uid = 30105
last_indexed_uid = 30103 | last_indexed_uid = 30104

So Dovecot thinks it has indexed everything.

You could also monitor (e.g. tcpdump/wireshark) the network traffic between Dovecot <-> Solr what happens when a new mail arrives. I suspect Dovecot sends it to Solr, which for whatever reason just ignores the update.

################### TCPDUMP ####################################
POST /solr/dovecot/update HTTP/1.1
Host: localhost:8983
Date: Mon, 28 May 2018 10:18:05 GMT
Transfer-Encoding: chunked
Connection: Keep-Alive
Content-Type: text/xml

<add><doc><field name="uid">37581</field><field name="box">e0c58a3093235153110800003ea484a8</field><field name="user">username</field><field name="id">37581/e0c58a3093235153110800003ea484a8/username</field><field name="body">Search Pattern: Kai8oovi

</field></doc></add>

And Dovecot sends the mail.

######### SOLR'S RESPONSE ###############
<?xml version="1.0" encoding="UTF-8"?>
<response>

<lst name="responseHeader">
<int name="status">0</int>
<int name="QTime">0</int>
</lst>
</response>