Laravel Filament Sticky Tabs aka Persistent or Cached tabs.

Resource.php

<?php

public static function form(Form $form) : Form
{
  return $form->schema(Tabs::make('Organizations')
                    ->tabs([
                        Tab::make('Tab 1')
                            ->schema([...]),
                        Tab::make('Tab 2')
                            ->schema([...]),
                        Tab::make('Tab 3')
                            ->schema([...]),
                    ])->reactive()
                );
}

tabs.blade.diff.php

// For ease, here's what's changed over the 'base' tabs component, I added: 

// wire:click="dispatchFormEvent('tabs::setActive', '{{ $tab->getId() }}')"
// circa line 36.

tabs.blade.php

// Put in: resources/views/vendor/filament/components/tabs.blade.php
<div x-data="{

    tab: null,

    init: function() {
        this.tab = this.getTabs()[@js($getActiveTab()) - 1]
    },

    getTabs: function() {
        return JSON.parse(this.$refs.tabsData.value)
    },

}"
  x-on:expand-concealing-component.window="
        if (getTabs().includes($event.detail.id)) {
            tab = $event.detail.id
            $el.scrollIntoView({ behavior: 'smooth', block: 'start' })
        }
    "
  x-cloak {!! $getId() ? "id=\"{$getId()}\"" : null !!}
  {{ $attributes->merge($getExtraAttributes())->class([
          'filament-forms-tabs-component rounded-xl shadow-sm border border-gray-300 bg-white',
          'dark:bg-gray-800 dark:border-gray-700' => config('forms.dark_mode'),
      ]) }}
  {{ $getExtraAlpineAttributeBag() }}>
  <input type="hidden"
    value='{{ collect($getChildComponentContainer()->getComponents())->filter(static fn(\Filament\Forms\Components\Tabs\Tab $tab): bool => !$tab->isHidden())->map(static fn(\Filament\Forms\Components\Tabs\Tab $tab) => $tab->getId())->values()->toJson() }}'
    x-ref="tabsData" />

  <div {!! $getLabel() ? 'aria-label="' . $getLabel() . '"' : null !!} role="tablist" @class([
      'rounded-t-xl flex overflow-y-auto bg-gray-100',
      'dark:bg-gray-700' => config('forms.dark_mode'),
  ])>
    @foreach ($getChildComponentContainer()->getComponents() as $tab)
      <button wire:click="dispatchFormEvent('tabs::setActive', '{{ $tab->getId() }}')" type="button"
        aria-controls="{{ $tab->getId() }}" x-bind:aria-selected="tab === '{{ $tab->getId() }}'"
        x-on:click="tab = '{{ $tab->getId() }}'" role="tab"
        x-bind:tabindex="tab === '{{ $tab->getId() }}' ? 0 : -1"
        class="flex items-center gap-2 p-3 text-sm font-medium filament-forms-tabs-component-button shrink-0"
        x-bind:class="{
            'text-gray-500 @if (config('forms.dark_mode')) dark:text-gray-400 @endif': tab !==
                '{{ $tab->getId() }}',
            'bg-white text-primary-600 @if (config('forms.dark_mode')) dark:bg-gray-800 @endif': tab ===
                '{{ $tab->getId() }}',
        }">
        @if ($icon = $tab->getIcon())
          <x-dynamic-component :component="$icon" class="w-5 h-5" />
        @endif

        <span>{{ $tab->getLabel() }}</span>

        @if ($badge = $tab->getBadge())
          <span
            class="inline-flex items-center justify-center ml-auto rtl:ml-0 rtl:mr-auto min-h-4 px-2 py-0.5 text-xs font-medium tracking-tight rounded-xl whitespace-normal"
            x-bind:class="{
                'bg-gray-200 @if (config('forms.dark_mode')) dark:bg-gray-600 @endif': tab !==
                    '{{ $tab->getId() }}',
                'bg-primary-500/10 font-medium': tab === '{{ $tab->getId() }}',
            }">
            {{ $badge }}
          </span>
        @endif
      </button>
    @endforeach
  </div>

  @foreach ($getChildComponentContainer()->getComponents() as $tab)
    {{ $tab }}
  @endforeach
</div>

Tabs.php

<?php

declare(strict_types=1);

namespace App\Filament\Components;

use Filament\Forms\Components;
use Illuminate\Support\Str;

class Tabs extends Components\Tabs
{
    protected string $view = 'filament::components.tabs';

    protected function setUp() : void
    {
        parent::setUp();
        // activeTab will throw a fit if it doesn't get an int/Closure, 
        // so let's ensure we have one, or go with default which is 1.
        $this->activeTab = (int) \cache()->get($this->getCacheKey()) ?? 1;
        $this->registerListeners([
            // Register a listener to trigger when tabs are clicked
            'tabs::setActive' => [
                function (self $component, string $newTab) : void {
                    // Let's make a list of all the tab names, usually something like _name, 
                    $tabs = \collect(
                        $component->getChildComponentContainer()
                            ->getComponents()
                    )
                        ->map(fn ($tab) => $tab->getId())->all();
                    // Let's grab the one that matches $newTab which is what was clicked.
                    // Again this must be an integer. We also add 1 because it's an array index
                    // and tabs start at 1.
                    $tab = \array_search($newTab, $tabs, true);
                    if($tab && is_numeric($tab)){
                      $newTabId = $tab+1;
                    }  
                    $newTabId = is_numeric($tab) ? ($tab+1) : 1; // default value;
                    \cache()->set(
                        $this->getCacheKey(),
                        $newTabId,
                        \now()->addMinutes(60)
                    );
                },
            ],
        ]);
    }

    public function getCacheKey()
    {
        $resourceName = Str::snake($this->getLabel()) ?? 'unknown_resource';

        return "{$resourceName}.activeTab";
    }
}