The core questions are:
1. At what tempo should the second movement of Beethoven's Fifth begin?
2. How should it be counted?
About Beethoven and tempo indications
At the time Beethoven composed the fifth symphony (1804–1808), the metronome had not yet been invented (1815).1,2 Although in 1817 he would go back and add metronome marking to his symphonies, at the time he composed the fifth, his attitude was that the metronome "is silly stuff; one must feel the tempos."3,4
This suggests that the tempo is genuinely up to the interpreter. In that case, it's worth asking a few experts what tempo they use.
What do various conductors do?
So what's the right tempo?
Based on the composers above, it seems that the questions comes down to whether one prefers to emphasize the andante end of things, in which case the tempo will be on the slower end of things, or the con moto, in which case the tempo will be a bit quicker. Even the marked tempo of 92bpm is worthy of consideration. It certainly fits the con moto bill.
In any case, Beethoven clearly intends this movement to allow for some relative calm after the excitement of the first, so any tempo must allow for that sense of being carried along gently.
How to count?
Consider that the 1 e & a counting pattern need not be strictly for sixteenth notes. Think of it as a way to count the quarter division of a beat. Thus, in 3/8 time, the 1 e & a would be applied to the 32nd notes — those being the fourth division of the basic eighth-note beat.
The movement contains no 64th notes, so they are not a concern.
What's the difference between 3/8 and 3/16 time when using a metronome.
There is no difference. As it only keeps the pulse, the metronome is only concerned with the numerator in the time signature and the bpm. At that level, 3/4, 3/8, 3/16, 3/32, 3/anything are all identical. The denominator relates to which notation corresponds to the pulse, so while it can have interpretive significance, once the tempo is chosen, the metronome reflects only that.
Notes
1Wikipedia entry for Beethoven's Fifth Symphony.
2"A Brief History of the Mechanical Metronome", by Charlene Kluegel, August 12, 2021
3"Reflections on Beethoven's metronome markings", by Martin Pearlman, n.d.
4Ibid. Emphasis mine.