My sense is that I can never think of an example of a piece published in the main era of classical music hand engraving (1800-1960) that has a tie which continues into the first ending where the engraver did not also put the ending of the tie in the second ending (similarly for other elements that extend into the first ending such as crescendi; I would also think that beams across the barline would behave similarly, but can't recall ever seeing one).
You are right that none of the most popular commercial software make it easy to notate this, though your approach with using an unconnected slur is pretty popular. For crescendi one would, I suppose, use two slopped lines that continue the slope of the crescendo that goes into the first ending. None of these elements would register properly in the semantics of the notation software, and playback can be very hard (I had to put in a separate, hidden, playback staff for this once with a rest at the beginning of the second ending as an approximation when I needed to do this once), but visually it's pretty good.
Much of musical notation remains ambiguously defined. For instance, there are cases where first and second endings extend over only part of a measure (ugh...): do accidentals carry into the second ending? Should a change of clef at the end of (or within) the first ending (or a key signature change; time signature change, etc.) be cancelled at the beginning of the second ending (my sense is that semantically the answer is no, but because the clef change at the end of the measure could catch the performer's eye, I would put in a courtesy restorative clef/key sig. etc.).