Migrating Joomla 3 to Joomla 4, 5 or 6 (Installatron)
Joomla 3 no longer receives (security) updates.
Installatron reports that you have the latest version, and that's correct: 3.10.12 is the final release of Joomla 3. Moving to Joomla 4, 5 or 6 isn't a regular update but a migration. That's why it isn't available through Installatron's update button.
Two things first
Don't raise the PHP version yet. Joomla 3.10 doesn't run on PHP 8.1 or higher: your site will break immediately. The right order is: migrate Joomla first, and only then raise PHP.
Your template and some extensions are the real job. Your current template is built for Joomla 3 and doesn't work on newer versions. The same goes for various plugins, such as the Nextend 2 slider. So every route involves a new template and setting up sliders and galleries again. Smart Slider 3 and Akeeba Backup do have modern versions.
Two possible routes
Route A: build from scratch (our advice for a small site). Use Installatron to install a fresh copy of the latest Joomla in a test location, for example a subfolder or subdomain. Choose a modern template there, move over the articles and menus, and rebuild the sliders and galleries. This new installation runs on a current PHP version right away. Once you're happy with everything, you put the new site live and remove the old one. Advantage: your current site keeps running in the meantime and you don't carry over any outdated leftovers.
Route B: migrate in steps (the official route). First make a full backup, with Akeeba or through Installatron. Then run the Pre-Update Check within Joomla 3.10, migrate to Joomla 4.4 and then move on to the latest version. Finally, raise the PHP version. Note: your template and extensions need new versions for this. If they don't have them, you'll need a new template with this route too and will have to rebuild parts of your site. This route mainly makes sense if you want to keep a lot of content or user accounts.
See also in the DirectAdmin guide: Creating and restoring backups in Installatron and Choosing the PHP version (Select PHP version).
Detailed explanation with screenshots: Cloning and creating a test environment (staging) in the DirectAdmin guide.