Agreed. I have always found this notation of ties to be quite clear. (Looking at it again I am a little surprised that the third bar needs a cautionary # in the pedal!)
third bar G Sharp is safe…
Just because the chord above where the G become Natural…
…and more, The soprano last note is Natural too…
So, could not be clearer!
I am in favor of this tie style as an option. They are effective because they reduce clutter without adding ambiguity or surprise. As a player, you read ahead far enough not to be fooled into releasing too early. It’s particularly sensible with the French style of reiterating accidentals on tied notes at the beginning of a bar (especially in organ music, of course).
I can’t see the original picture, but if these were so-called “French ties” (that is, the one broken between the starting and final note), add me about the enthusiasts!