The first thing I tried was upgrading the client to v.11  and the error continued.

We are getting null values in a variable/column where null values aren't allowed.

Log Name:      Laserfiche-ContentRepository-Service/Admin
Source:        Laserfiche-ContentRepository-Service
Date:          11/4/2022 12:37:35 PM
Event ID:      150
Task Category: None
Level:         Error
Keywords:      
User:          domain\user
Computer:      lfappserver.example.com
Description:
An error occurred when executing an SQL query, retrieving the results of a query, or otherwise communicating with the database server. Session ID=452; Dialog ID=53099; Repository="RepoName"; Function=SysAnnCreate; Message="[Microsoft][ODBC Driver 17 for SQL Server][SQL Server]Cannot insert the value NULL into column 'private', table 'LF_McAllen.dbo.ann'; column does not allow nulls. INSERT fails."; Statement="{call create_ann(:pageid<bigint,in>, :itemid<short,in>, :anntype<short,in>, :anncreator<raw[85],in>, :anncreated<timestamp,in>, :annlastmod<timestamp,in>, :annvisibility<int,in>, :anncomment<char[200],in>, :protect<short,in>, :ann_access<short,in>, :ann_reason_id<int,in>, :pos1<int,in>, :pos2<int,in>, :pos3<int,in>, :pos4<int,in>, :rotation<short,in>, :direction<short,in>, :color1<int,in>, :color2<int,in>, :color3<int,in>, :thickness<short,in>, :opacity<short,in>, :style1<short,in>, :style2<short,in>, :style3<short,in>, :stampid<int,in>, :attachstoreid<int,in>, :mime<char[127],in>, :filename<char[259],in>, :anntext<varchar_long,in>, :anntextsize<int,in>, :data1<char[600],in>, :annid<int,out>)}"; SQL Variable=""; SQL State="23000".
Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
  <System>
    <Provider Name="Laserfiche-ContentRepository-Service" Guid="{82fc23fe-4b0a-435c-82e6-01c7077098af}" />
    <EventID>150</EventID>
    <Version>0</Version>
    <Level>2</Level>
    <Task>0</Task>
    <Opcode>0</Opcode>
    <Keywords>0x4000000000000000</Keywords>
    <TimeCreated SystemTime="2022-11-04T17:37:35.210555900Z" />
    <EventRecordID>188</EventRecordID>
    <Correlation />
    <Execution ProcessID="6468" ThreadID="3368" />
    <Channel>Laserfiche-ContentRepository-Service/Admin</Channel>
    <Computer>lfappserver.example.com</Computer>
    <Security UserID="S-1-5-21-2538293913-1371282071-302991336-3607" />
  </System>
  <EventData>
    <Data Name="sessionID">452</Data>
    <Data Name="dialogID">53099</Data>
    <Data Name="repository">RepoName</Data>
    <Data Name="func">SysAnnCreate</Data>
    <Data Name="message">[Microsoft][ODBC Driver 17 for SQL Server][SQL Server]Cannot insert the value NULL into column 'private', table 'LF_McAllen.dbo.ann'; column does not allow nulls. INSERT fails.</Data>
    <Data Name="stmt">{call create_ann(:pageid&lt;bigint,in&gt;, :itemid&lt;short,in&gt;, :anntype&lt;short,in&gt;, :anncreator&lt;raw[85],in&gt;, :anncreated&lt;timestamp,in&gt;, :annlastmod&lt;timestamp,in&gt;, :annvisibility&lt;int,in&gt;, :anncomment&lt;char[200],in&gt;, :protect&lt;short,in&gt;, :ann_access&lt;short,in&gt;, :ann_reason_id&lt;int,in&gt;, :pos1&lt;int,in&gt;, :pos2&lt;int,in&gt;, :pos3&lt;int,in&gt;, :pos4&lt;int,in&gt;, :rotation&lt;short,in&gt;, :direction&lt;short,in&gt;, :color1&lt;int,in&gt;, :color2&lt;int,in&gt;, :color3&lt;int,in&gt;, :thickness&lt;short,in&gt;, :opacity&lt;short,in&gt;, :style1&lt;short,in&gt;, :style2&lt;short,in&gt;, :style3&lt;short,in&gt;, :stampid&lt;int,in&gt;, :attachstoreid&lt;int,in&gt;, :mime&lt;char[127],in&gt;, :filename&lt;char[259],in&gt;, :anntext&lt;varchar_long,in&gt;, :anntextsize&lt;int,in&gt;, :data1&lt;char[600],in&gt;, :annid&lt;int,out&gt;)}</Data>
    <Data Name="sqlvar">
    </Data>
    <Data Name="sqlstate">23000</Data>
  </EventData>
</Event>

That column was supposed to be dropped during the upgrade process - it was replaced by the ann_visibility column. It sounds like something went wrong during upgrade. There should be more information in the event viewer from the time that you performed the upgrade.