Quick question about active crossover

One decoupling capacitor per supply per chip.
That's the rule for fast logic certainly, where edges are a few nanoseconds, but slow analog isn't necessarily so demanding - dI/dt for fast logic can be of the order of 10A/µs (driving a 20mA LED at 2ns rise time), and that's way beyond anything an analog audio amp produces. So the stray inductance between a logic chip and its decoupling caps has to be made as small as possible for logic, requiring a decoupling cap on each supply pin (within a few mm).

Of course instabilities in audio circuits can involve much higher dI/dt than normal operation, for instance fast opamps often get treated like fast logic.

However I'd suggest go to the datasheet first - the manufacturer recommendation will be backed by rigorous testing.