This is the Plex monitoring script that wrote and have been using since +/- 2017. I cribbed the list of processes to kill and the idea of checking that the web UI responded without error from other people's scripts but the rest is all me.

plex-monitor.ps1

#Start-Transcript -Append -Path .\plex-monitor-transcript.log -IncludeInvocationHeader:$false -Force

<#
    This is my Plex monitoring script. There are many like it, but this one is mine. If 
    you're running Plex as a Windows Service this script is not for you as-written, but 
    you could possibly modify it to work for you by commenting out the Start-Process 
    line, configuring the service to automatically restart, and coming up with a 
    different way to keep the script running.

    This updated version should automatically discover the Plex installation path and 
    maintenance window times. If it can't, it's probably not running under the same 
    user account that was used to install Plex.

    This version also writes to a log file. The path and name of the file will be the 
    same as the script, with the extention changed to .log

    For my setup, the computer running Plex is configured to auto-login as 'plexuser' 
    and a Scheduled Task launches the script when the user logs in or connects via RDP.
        General:
            * Run only when user is logged on.
        Triggers:
            * At log on (of Plex user)
            * On connection to a user session (of Plex user)
        Actions:
            * Start a program
            * Program: powershell.exe
            * Add arguments: -file [path-to]\plex-monitor.ps1
        Settings:
            * Allow task to be run on demand
            * If the running task does not end when requested, force it to stop
            * If the task is already running: Do not start a new instance

    When performing a manual Plex update, stop the script. If you perform automatic updates 
    then they should run during the maintenance window and the script will ignore the 
    downtime, but I've not personally tested that scenario.
#>

function Get-PlexPath {
    try {
        $plexInstallFolder = Get-ItemPropertyValue -Path 'HKCU:\Software\Plex, Inc.\Plex Media Server' -name 'InstallFolder'
        if ((Test-Path "$plexInstallFolder\Plex Media Server.exe") -eq $true) {
            return "$plexInstallFolder\Plex Media Server.exe"
        }
    } catch {
        # This would discover the default installation path, but that's not really wanted. If the 
        # registry key doesn't exist then this script is probably running as the wrong user.

        #if ((Test-Path "$env:PROGRAMFILES\Plex\Plex Media Server\Plex Media Server.exe") -eq $true) {
        #    return "$env:PROGRAMFILES\Plex\Plex Media Server\Plex Media Server.exe"
        #}
    }

    return $null

}

function Get-PlexMaintenanceWindow {
    $ButlerStartHour = 3
    $ButlerEndHour = 7
    try { 
        $ButlerStartHour = Get-ItemPropertyValue -Path 'HKCU:\Software\Plex, Inc.\Plex Media Server' -name 'ButlerStartHour'
        $ButlerEndHour = Get-ItemPropertyValue -Path 'HKCU:\Software\Plex, Inc.\Plex Media Server' -name 'ButlerEndHour' 
    } catch {
        # Nothing
    }

    return "$($ButlerStartHour):00", "$($ButlerEndHour):00"
}

$PlexExePath = Get-PlexPath
$PlexUri = 'http://localhost:32400/web/index.html'
$MaintenanceStart, $MaintenanceEnd = Get-PlexMaintenanceWindow
$LogPath = (Get-Item $PSCommandPath).DirectoryName + "\" + (Get-Item $PSCommandPath).BaseName + ".log"

if ($null -eq $PlexExePath) {
    "Could not locate Plex executable." | Tee-Object -FilePath $LogPath -Append 
    return
}

$progressPreference="SilentlyContinue"

$dt=(get-date -Format u).replace("Z", "")

"$($dt): Startup." | Tee-Object -FilePath $LogPath -Append 

# Give time for system to settle / Plex to start.
Start-Sleep -Seconds 180

# Give the Maintenance Window a few minutes buffer.
$min = (Get-Date $MaintenanceStart).TimeOfDay.TotalMinutes - 2
$max = (Get-Date $MaintenanceEnd).TimeOfDay.TotalMinutes + 5

While ($true) {
    try {
        Invoke-WebRequest -Uri $PlexUri -TimeoutSec 30 -UseBasicParsing -DisableKeepAlive | Out-Null
    } catch {
        $global:ex = $_
        if ($ex.Exception -like '*401*Unauthorized*') {
            # This is the expected result if authentication is required.
        } else {
            $now = (Get-Date).TimeOfDay.TotalMinutes

            if ($now -le $min -or $now -ge $max) {
                $dt=(get-date -Format u).replace("Z", "")
            
                #Write-Host "$($dt): Plex non-responsive, stopping Plex processes."
                "$($dt): Plex non-responsive, stopping Plex processes." | Tee-Object -FilePath $LogPath -Append 

                Get-Process "Plex Media Server" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue
                Get-Process "Plex Transcoder" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue
                Get-Process "Plex Relay" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue
                Get-Process "Plex Tuner Service" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue
                Get-Process "Plex Media Scanner" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue
                Get-Process "PlexScriptHost" -ErrorAction SilentlyContinue | Stop-Process -Force -ErrorAction SilentlyContinue -PassThru | Wait-Process -Timeout 30 -ErrorAction SilentlyContinue

                $dt=(get-date -Format u).replace("Z", "")

                #Write-Host "$($dt): Starting Plex."
                "$($dt): Starting Plex." | Tee-Object -FilePath $LogPath -Append 

                Start-Process $PlexExePath

            } else {

                $dt=(get-date -Format u).replace("Z", "")
                #Write-Host "$($dt): Plex non-responsive during maintenance window."
                "$($dt): Plex non-responsive during maintenance window." | Tee-Object -FilePath $LogPath -Append 
            
                # Sleep until maintenance window closes.
                $untilSec = $max * 60 # (Get-Date $MaintenanceEnd).TimeOfDay.TotalSeconds
                $nowSec = $now * 60 #(Get-Date).TimeofDay.TotalSeconds
                $sleepSec = [int] ($untilSec - $nowSec)

                $dt=(get-date -Format u).replace("Z", "")
                #Write-Host "$($dt): Sleeping for $($sleepSec) seconds"
                "$($dt): Sleeping for $($sleepSec) seconds" | Tee-Object -FilePath $LogPath -Append 
                
                Start-Sleep -Seconds $sleepSec
                
                $dt=(get-date -Format u).replace("Z", "")
                #Write-Host "$($dt): Waking."
                "$($dt): Waking." | Tee-Object -FilePath $LogPath -Append 
            }

            Start-Sleep -Seconds 60
        }
    }
    Write-Verbose 'Sleeping.'
    Start-Sleep -Seconds 5
}
#Stop-Transcript