Appsliprotate.prc and statusbarlib.prc are both only installed into RAM and not ROM. They were not part of the update to the SD card and they were files that P1 designed to work with the T3.
The two files must be installed at the same time and if done correctly - they will force a soft reset. Both files are dated around 9/17/03 but will only reflect the date installed if you use our good friend FileZ. These two files would be missing from RAM or would have an August of 2003 date if they are the older versions on your T3.
Now for the bad news, since they are part of RAM they are not safe from a hard reset. They will be typically reinstalled during a normal restore from a hard reset so not to worry. This can also be a good thing....because if your not certain that you have the latest versions then you can hard reset the device and then install the latest Sept 2003 versions afterwards and you then know your good to go.
The version number of the OS prior to the SD ROM update was 5.2.1 . The version did not change as a result of the update for the SD problem. You can download the update from P1 and attempt to run it....if it's already been installed it will not reinstall and no damage will be done. I'm not certain what files were changed in the SD process but it was a Flash to ROM so it would be restored upon a hard reset.
Good luck with the T3 and let me know if you want some additional info......if you try the TomTom on it - I'd like to know your opinion of it's ease of use.
EDIT: After re-reading your post it appears that you tried to run the update and it stated "already installed" then with regards to the T3 update then your good to go. Add FileZ to the RAM and then check the dates on the appslip and statusbar files they will probably show the last date when installed but if you added them from Datebk5 web site - they are the latest versions so your probably good to go.
The only thing else would be to check the Support Page at P1 for the T3
here but don't forget I'm giving you the English page. I don't know if there is a different one for Sweden/Denmark that you'd use. I'd be certain to download and install the Outlook conduits if your using it and the upgrade to the Palm Desktop/Hotsync manager.