@super_simon123 It is probably too late, but I made it work with following code (using LiveWire 3):

<div>
    <div class="px-4 mb-4">
        <div>{{ $selectedYear - 1 }} orders: {{array_sum($lastYearMonths->toArray()) }}</div>
        <div>{{ $selectedYear }} orders: {{array_sum($thisYearMonths->toArray()) }}</div>
    </div>


    <div class="p-4">
        <div class="w-40 mb-4">
            <label for="selectedYear" class="block mb-2 text-sm font-medium text-gray-900">Select a year</label>
            <select wire:model.live='selectedYear' id="selectedYear" class="bg-gray-50 border border-gray-300 text-gray-900 text-sm rounded-lg focus:ring-blue-500 focus:border-blue-500 block w-full p-2.5">
                @foreach($availableYears as $year)
                    <option value="{{ $year }}" {{ $selectedYear === $year ? 'selected' : '' }}>{{ $year }}</option>
                @endforeach
            </select>
        </div>

    <canvas id="myChart"></canvas>
</div>


@script
<script>

        const ctx = document.getElementById('myChart');

        const myChart = new Chart(ctx, {
            type: 'bar',
            data: {
                labels: ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'],
                datasets: [{
                    label: `${$wire.selectedYear - 1} Orders`,
                    backgroundColor: 'lightgray',
                    data: $wire.lastYearMonths,
                }, {
                    label: `${$wire.selectedYear} Orders`,
                    backgroundColor: 'lightgreen',
                    data: $wire.thisYearMonths,
                }]
            },
            options: {
                scales: {
                  y: {
                    beginAtZero: true
                  }
                }
            }
        });

        Livewire.on('updateTheChart', () => {
            myChart.data.datasets[0].label = `${$wire.selectedYear - 1} Orders`;
            myChart.data.datasets[1].label = `${$wire.selectedYear} Orders`;
            myChart.data.datasets[0].data = $wire.lastYearMonths;
            myChart.data.datasets[1].data = $wire.thisYearMonths;

            myChart.update();
        });

</script>

@endscript

In livewire 3 you have to replace emit with dispatch:

$this->dispatch('updateTheChart');

And I am using a lifecycle hook:

    public function updatedSelectedYear()
    {
        $this->updateOrdersCount();
    }

I am a beginner at Laravel myself, so maybe I am doing something wrong but it works.

thisYearOrders is called thisYearMonths and the same with lastYearOrders (handling months without orders).

Dynamic Charts with Livewire and Alpine