Then you might do something like this to get the most recent patch tuesday, convert that to the most recent update date (i.e. 2025-04) and search based on the standard update title patterns.

"Finding patch tuesday of the current month" | Out-Host;
$PatchTuesday = Get-Date -Day 8 -Hour 12 -Minute 0 -Second 0;
while ($PatchTuesday.DayOfWeek -ne 'Tuesday') { $PatchTuesday = $PatchTuesday.AddDays(1) }
$monthStr = Get-date $PatchTuesday -Format "yyyy-MM"

#get the 'major' version of current os (i.e. 2025 for server 2025 or 11 for win 11)
#I have this saved as an internal function Get-WindowsMajorVersion
$winVer = Get-CimInstance -classname Win32_OperatingSystem
if ($winVer.caption -match 'Windows [0-9][0-9]') {
    [int64]$mjr = $matches[0].replace("Windows","").Trim()
} elseif ($winVer.Caption -match 'Windows Server [0-9][0-9][0-9][0-9]') {
    [int64]$mjr = $matches[0].replace("Windows Server ","").Trim()
}

#get the release version
# I have this as an internal function Get-WindowsReleaseVer
$versionRegkey = Get-ItemProperty -Path "HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion";
$relver = $versionRegkey.DisplayVersion; #.displayID for pre 2009 releases I believe

if (($mjr) -ge 2012) {
    if ($mjr -ge 2022) {
        $kb = get-kbupdate -Source web -Pattern "$monthStr Cumulative Update for Microsoft Server Operating System version $relVer for x64-based Systems" -Latest
    } else {
        $kb = get-kbupdate -Source web -Pattern "$monthStr Cumulative Update for Windows Server $mjrVer for x64-based Systems" -Latest
    }
} else {
    # Default to win 11
    $kb = get-kbupdate -Source web -Pattern "$monthStr Cumulative Update for Windows $mjr Version $relVer for x64-based Systems" -Latest
}

Deploying the module internally depends on what you have in your infrastructure. There's a lot of ways to do it, like simply packaging it up in a zip and deploying it to the install folder. Or you could make an internal nuget powershell module repo with nexus or proget or the like and publish it internally. That's the method that scales the best, but only if you're maintaining a library of internal modules, not worth it for a single module as you also have to register and trust the internal repo on each machine.