Summary: For me learning by doing with good callouts and short, high point briefing before worked great. I also usually use a similar style of prompting people to do things when I am teaching people IT stuff instead of doing it for them or only talking about it (family tech support, might be a chaotic raid, but usually less twitchy /s).
As a datapoint in a similar situation, I played in a guild in Lost Ark that was quite competitive (more than I was). This game has mechanic heavy raids, but I do not know how they compare to Destiny 2. I went into early raids essentially blind and learned mostly by doing and listening to good calls during it.
A few minutes before we went in, and during the straightforward way to the bosses, someone familiar with the mechanics explained the general idea, e.g. "there is an instant kill in all phases, in the first 2 you need to stand on the whitish spots, in the 3rd phase on the reddish spots". During the actual encounters, and before the switch of mechanics, they would call out in short what to do, e.g. "stand in red" or just "red".
I personally liked this way. It gave me a rough idea what to expect and refreshed my memory enough to not screw up in the heat of the moment. The explanation itself was also quite short, because we didn't go through the play by play, only covering the important stuff and relying on in the moment callouts. Plus, some briefing happened during the run to the boss. This method might only work with a somewhat competent/disciplined group. We played like this as a guild with good raid leaders and during crunch time we had good comms discipline. In addition we went into training raids with inexperienced players, with the expectation that we might not make it, but still try our best, and usually won. There also were more or less fixed raid teams that grinded these bosses without any explanation, because everyone had done it multiple times already.
I played another game with lightly mechanics based bosses and I, or someone else, explained in about 3 chat messages what to do when we went in with randoms. It was simple enough "I do X, shoot adds when I do X, if I die, do Y". The experienced players took care of the harder/mechanics parts, everyone else covered the easy parts. If you have a semi-fixed group for this, everyone learns all mechanics at some point by observing.
Edit: Typo