the breath is part of the music, the music has to breathe, for any instrument...

The breathing really is part of the phrasing and NEEDS to be there.

While I agree that most composers - even contemporary ones - are aware that woodwind and brass players have to breathe, I feel that "breath is usually part of the melody". For non-melodic parts - especially tuba - breathing is probably the most challenging aspect and I envy tuba players who can use circular breathing. For lesser mortals it is usual to stagger breathing between players and to leave notes out in order to retain the musical feel.

I think one should expect an increasing number of especially solo works for flute which assume that the player can use circular breathing effectively - at least for an extended moving passage if not for a single sustained note when an imperceptible join is difficult.

Frankly, I'm rarely impressed with technically challenging works and prefer music which I find moving.

An alternative to water/straw is to blow in front of a pending long ribbon of rice paper (or similar very light paper). The paper should stay "blown" away" while CB. This requires more air than the straw thing, I guess, but probably resembles more the case of playing the flute than bubbling into water....

A good number to aim for is about 30 seconds with ease. This will cover most any music that you might encounter and virtually any player can get to this level.

The way I practiced was to hold my breath and double what I was aiming for. ie - it's usually that you run out of oxygen/need to breathe before your lungs run out of air. Some players can hold their breath for two minutes or more.