If you want to look at a compound melody as two separate parts, or if you want to look at an arpeggiated part as a sustained chord, rewrite the parts involved and rhythmically shift parts so they realign with the chord changes, which will normally be on the beat. We can do this to your bass clef in stages:
First beak apart the beaming so that the notes are literally two separate parts. In this case the tenor becomes syncopated, so we move it back a half beat to realign with the on beat chord changes.
...Here the bassline alternates with the tenor on the upbeats and this causes the G# on upbeat 2 to move to the G# on downbeat 3 ... That the tenor and bass both progress to G#...
After you beak up the compound (really it's a broken chord texture) you can see the "tenor" part is really a repeating G#3. It is not moving so it cannot be part of any forbidden relative motion.
Anyway, you can keep reducing the bass clef part until you get to a "three part" chord in whole notes. At that point the treble clef at beat 2 can then be regarded as a appoggiatura chord embellishing the G#m chord. It seems worthwhile to reduce the texture all the way to whole notes, because it sort of confirms what can be heard in the original form. In the original the C#m chord on beat two is on the beat against a D# bass and dissonant. Instead of looking for some exotic chord identity involving all pitches as chord tones of some extended chord, it's simpler to recognize everything in the bass clef indicates only one chord for the whole measure. This is important regarding the concerns of relative motion, because the only real motion occurring is oblique motion when D#4 B4 make the auxiliary move to E4 C#5 and back.
Back to the title question.
Can compound melodies cause voice leading errors? "Chordal skips" in my harmony textbook...
If your book says to not disguise bad relative motion with broken chord motion or compound lines, then don't do that in the book's lessons. But, in real common practice era scores you will see broken chord motion used to mitigate parallel motion.
A lot of your questions stem from the textbooks you choose. It's clear you are interested in 18th century practices, but you use modern textbooks, and some of those you have mentioned in the past seem to have a jazz orientation. Try using textbooks that are either specialized on the 18th century or just get modern, translated editions of historical textbooks. Michael Callahan's Techniques of keyboard improvisation in the German Baroque and their implications for today's pedagogy (https://urresearch.rochester.edu/institutionalPublicationPublicView.action?institutionalItemId=13844) and Niedt's Musical Guide (https://archive.org/details/musicalguide0000nied/) are good examples.
The following is from Niedt's guide...
After the model passage there are many examples of how to play the chords with many different broken chord patterns. There are two things to point out.
First, example XI shows parallel fifth circled in red. This would be an example of how broken chord patterns or compound line may introduce forbidden parallels into an otherwise OK voice leading chord skeleton.
Second, read Neidt's comment highlighted in yellow. Notice is annoyance with "fifth-hunters" and how they mistake what is important (in this case how to enliven a simple chord structure with rhythmic and melodic motion) and focus instead on a fleeting instance of parallel fifths.
From a technical point of view, I think it needs to be mentioned that if the passage were reduced to four parts it would be...
...and we can see the "parallel" motion is the result of mistaking the soprano part for the alto part in the single notes line arpeggiating the chords.
