how do I update Firefox

Normally, you can find the update from menu - help - about Firefox - what's new

You will see a get Firefox button.

If the above not possible, you can https://support.mozilla.org/en-US/kb/update-latest-version-firefox-android

No there is no update button there its just help articles and my device doesn't support google play services

Show me the screenshot. It could be a download icon. If your device doesn't support Google play. You can download the app file directly from Mozilla: https://support.mozilla.org/en-US/kb/install-firefox-your-phone-or-tablet

It's possible that without any of the store's backend you'd need to manually update yourself over and over.

The APK/AAB bundles are available, and are either platform/architecture specific, or if you don't mind bigger downloads there are also universal ones to simplify the process a bit.

For v150.0.2 they are here: https://ftp.mozilla.org/pub/fenix/releases/150.0.2/android/fenix-150.0.2-android/

(try whichever one works for your device, I'd start with the "universal" APK personally…)