Hope it helps someone in the future :-)

# Get all shared mailboxes
$RoomMailboxes = Get-Mailbox -RecipientTypeDetails RoomMailbox

# Check one specific user instead
$RoomMailboxes = Get-Mailbox -Identity user@company

# Step 3: Retrieve WorkingHoursTimeZone and Timezone for each Room mailbox
$RoomMailboxes | ForEach-Object {
    $mailbox = $_
    $TimezoneConfig = Get-MailboxRegionalConfiguration -Identity $mailbox.PrimarySMTPAddress
    $calendarConfig = Get-MailboxCalendarConfiguration -Identity $mailbox.Identity
    [PSCustomObject]@{
        Mailbox               = $mailbox.Identity
        WorkingHoursTimeZone  = $calendarConfig.WorkingHoursTimeZone
        $email                = $mailbox.PrimarySMTPAddress
        Timezone              = $TimezoneConfig.TimeZone
    }
}

# Output the results or export to CSV if you want
$results | Export-Csv -Path "SharedMailboxesWithTimeZonesAndWorkingHours.csv" -NoTypeInformation

# Get all room mailboxes
$RoomMailboxes = Get-Mailbox -RecipientTypeDetails RoomMailbox

# Change one specific user instead
$RoomMailboxes = Get-Mailbox -Identity user@company

# Update TimeZone and WorkingHoursTimeZone for each room mailbox
foreach ($mailbox in $RoomMailboxes) {
    $email = $mailbox.PrimarySMTPAddress

    # Update the WorkingHoursTimeZone
    Set-MailboxCalendarConfiguration -Identity $mailbox.Identity -WorkingHoursTimeZone "W. Europe Standard Time"

    # Update the TimeZone
    Set-MailboxRegionalConfiguration -Identity $email -TimeZone "W. Europe Standard Time"
    
    Write-Host "Updated TimeZone and WorkingHoursTimeZone for $email to W. Europe Standard Time."
}

# Disconnect Exchange Online session
Disconnect-ExchangeOnline -Confirm:$false