The notated value of grace notes at the end of a trill is conventional, though it is usually approximately correct (e.g. you are more likely to see 32nd-notes in a slow movement than in a fast one).
The termination of the trill should be at the same speed as the trill itself.
That said, if you can play triplets (or 32-notes as suggested in a comment) for the first part of this trill, your tempo for the whole movement is too slow. It's "Presto Agitato", not "Allegro Con Brio!". The 16th notes should be as "fast as you can play them."
Nine notes, including the turn, is about as many as will fit into the complete trill at the proper tempo. There is no reason why the speed of a trill ever needs to fit like clockwork with simultaneous written notes. In fact if you think the trill plus a turn has any melodic function, it would be perfectly reasonable to play fewer notes than the written-out 16ths - i.e a seven-note trill.
Incidentally, in the first edition the preceding trills (with the octave note below) have written turns, but this one does not. Some editor wrote the turn you are asking about, not Beethoven. The corresponding trill in the recapitulation does have a turn in the first edition, but that isn't much of an excuse for tidying up the score using "copy-and-paste" editing!
