Heavy Pressure card text reads: "Exhaust this card when a hero would suffer (Damage) from an attack. Instead of suffering (Damage), that hero suffers an equal amount of (Strain)."

Does this also apply to indirect damage resulting from an attack i.e. Cleave, Blast? For example, if my AT-ST attacks a Rebel figure and surges for 2 Blast, can I use this card to put 2 Strain on one of the adjacent Heroes instead?

No.

"From an attack" means damage suffered by the target during step 7 of the attack.

Otherwise it would not have "from an attack" at all.

I was thinking that technically it IS damage suffered from an attack, just not 'during an attack'. Many abilities have the timing 'during an attack', which leads me to think that maybe 'from an attack' is more broad...

You can think that Blast and Cleave are just attack-related abilities which are resolved after attack resolves.