The Beethoven Trio we are looking at is in Sonata form, revolves around I and V. The other commonly used chords are viio7/V, N, and Ger+6.
The German Augmented 6th functions as a predominant while the Neopolitan funtions as a dominant. Beethoven spells the German Augmented 6th two ways: as is, and respelled as a V7/N.
Ex: In B major, we see a C#o7. C#o7 is not naturally occuring, and it’s fully diminished so it’s not borrowed from minor. Now we have to look at context.
The chords surrounding the C#o7 are Ebm - Bb/D - A#o/C# - B - F#7/C# - C#o7 - C7. We are in Ebm: i - V6 - viio6/VI (modulates to viio6 in B major) | B:viio6 - I - V43 - [IVI:1] (between the C#o7 and C7).
This section is a sequence, where Beethoven was looking for chords with very close voicings. The only way to explain the C#o7 is with IVI: idealized voice-leading interval, or how many half-steps it takes to get from once chord to the other. IVI is also called TVD, or total voice-leading distance.
Because C#o7 is a symmetrical chord, you have the option of using C#o7, Eo7, A#o7, and Go7. In B, we can think of it as a borrowed viio7 (A#o7) to pivot into F by calling it a viio7 (Eo7) in F. Once we pivot, our chords are Eo7, C7, F, in Fmajor (viio7 - V7 - I). Beethoven uses this C#o7 chord sequence to modulate from 6 flats (Eb minor), to 5 sharps (B major), to 1 flat (F major) .