In the first bars of the Barcarola et Scherzo by Alfredo Casella the piano part has chords with legato, tenuto and staccato signs all together:
What is the correct way to play these notes? What could be the intent of the author? It does not seem a portato (when you have several notes with both staccato and legato) like this.
The combination of a staccato dot with a tenuto marking would normally indicate the that the chords are to be played portato, with a small gap between them. The slurs clearly contradict this.
When faced with contradictory markings in a piece of music the most expedient solution is to simply play whatever makes most musical sense to the performer. I would leave a very small gap (just the time it takes to lift the hand) but still make it clear that each pair of chords are one musical idea. The exact phrasing in the piano is probably not so critical: the piece is a flute solo and that's what everybody will be listening to.
Before someone suggests asking the composer: he died in 1947, but this does have the advantage that he's not going to turn up at your concert and complain that you're not playing the piece properly.
The notation, to the best of my knowledge, is idiosyncratic, and clearly the score doesn't offer its meaning. Since it appears in both the piano (as shown in the question) and flute (below, m. 17), it clearly needs to have a meaning for both instruments.
Listening to a couple of YouTube recordings (Uri Shoham; Mario Caroli), the interpretation is that it represents a weakly accented note. That is, it's an indication to "lean" into the note a bit, but not a full-on accent.
