The small AirTags get a small update, namely to version 1.0.276 build 1A287b. If you still remember that Apple improved the anti-stalking function of the AirTags a bit with the last updated firmware at the beginning of June, you will notice that the version number has remained the same and only the build number has changed. So this can only be a small improvement.
The installation of the new firmware is done automatically, as long as the AirTags are close enough to the paired iPhone. Manual nudging is not possible. There are cases where an update does not take place – in this case, it is simply a case of sitting out the problem.
If you are interested in the current software version of your AirTags, you can do so by simply tapping on the battery indicator of the AirTags: then you can see the version number (but not the build number).