Other than the current participation in the World Rally Championship its not clear what Albert's current projects and duties are. It doesn't look as if he is still studying or doing any sort of placement with financial/asset management companies etc.
I'm guessing that the Thurn und Taxis Forst (Forestry) is something he is involved in/leading on because he is the only one featured on the website.
As regards St Emmeram and all Regensburg office based control of their business I'm guessing that he does a share - but from what can be gathered Regensburg might be his primary address (as his sisters primary address is London) but he could be living in Rome or Zurich possibly running the non Schloss business interests.
Alternatively he could be doing little as the 3 children he has the least known duties (despite in theory having the most predestined). Maria is Artist-Housewife -Wife & Mother and Elizabeth documents her life on Instagram daily as Fashionista-Socialite-writer-traveller who does some charity and helped design some shoes. Albert races maybe 6 weekends a year and attends 2 or 3 events a year (a Gotha funeral or the Bavarian Ministers Summer Party).
Now just my opinion but Albert comes across as quite shy and as Gloria "sells " means Gloria is still No1 in anything relating to the Scholes- so it suits him to not be front and centre with St Emmeram and estate/Bavarian interests.
BUT I think being a) by now 33 with a good 15 years of perusing his racing & b) also probably as much business education as he is going to get he should really starting acting like the Head of his own Family House.
Albert is unmarried so Gloria being the Chatelaine and the right hand in his business affairs is to be expected but the level of prominence Gloria has is more than a consort, a regent or Furst's mother -until recently on the website you would be forgiven for thinking she was an heiress of the Thurn und Taxis's in her own right - the equivalent of the Duchess of Alba.
The 500 year story of the Thurn und Taxis's is filled with strong women who stepped up to steer the family fortunes - Therese, Helene and especially Gloria - but it is a story of male primogeniture where women are the caretakers.
Until now it has been fathers, sons and grandsons who sought to build their fortunes. Albert's own father experimented in ventures and undertook two heart transplants just to hold on in order to steer the business a little longer so his son could follow in their footsteps.
If Johannes had lived he would have been 90 this year but would have probably made Albert spend the last 15 years taking on a similar role to Prince Ernst of Hannover and which Johannes himself did for his family. Gloria would have probably done her Schlossfestspiel but I don't think a lot of what seems to be Head of the House duties would have been undertaken by her in Regensburg and Bavaria.
During the 1990-2001 period when Gloria and others appointed to oversee Albert's inheritance things seemed quite traditional - investing and divesting for Albert to take the reins of a healthier business empire. The expectation was probably that Albert by 25 would be quite entrepreneurial in his own right (the only known example of this is the solar farm) as his father had been.
Instead as soon as Albert got control he looked as if he handed it to Gloria and the Schlosses were made to pay for themselves by becoming a venue for weddings, Christmas fayres, garden fayres, music festivals, schools and nursing homes.
The trouble is the media trumpet the fact that the investments survived because of Gloria and the above ventures are successful because they are run by Gloria and attended by Gloria. Gloria comes across as wonder woman without whom everything would crumble and Albert the not often seen playboy not very important son of said wonder woman.
Albert either needs to get a wonder woman of his own in order for Gloria to pass the torch to or else he needs to be seen as a businessman & figurehead of his own family - it might not be his thing but he needs to have his own "era" at St Emmeram or what was all the enterprising family work for?