I am writing a harpsichord score, and I want to be quite specific with note durations: most notes should be held for the duration of the following note (see bar 1). I am afraid that explicitly writing the durations like this (bar 1) might be unnecessary complicated, and I was wondering if there is a way to simplify, for instance not writing the ties and simply indicate that the notes should be held? I think I remember seing the indication laisser résonner somewhere? (see bar 2) Is bar 1 overly complicated or is it a proper way to write the sound that I'm trying to get?
Yes, bar 1 is overly complicated, but not in the way that you think. You need to respect the beats in the bar better, because consolidating the note values in that fashion is very hard to read.
No, you don't want to use laisser vibrer or laisser résonner, because that implies that all the notes are held, and the harpsichord doesn't have a pedal to raise the dampers. That means that your performer will have to try to hold all the notes in the measure with his/her fingers, which means 5-note chords in both hands that aren't particularly grateful to finger (note the black keys under the short fingers). It is also not what you are intending.
Try something like this:
In the right hand, the addition of a second voice is cleaner. Note that the first half of the measure uses a simple 1:2:1 proportion - that's about the only exception to notating each beat that exists. The 1:2:1 proportion has been notated that way in keyboard music for a very long time. The other off-beats are using ties across the beat boundaries, which is both normal and much easier to read.
You can notate the left hand as one voice with chords if you want (i.e., the high G♯ dotted quaver attached to the E, no rests, and the stems changing direction according to the vertical position of the notes) - it is six of one, a half-dozen of the other which is more legible.