I believe bleed air has to be cooled before entering the cabin, which under some conditions could condense some of the water content out resulting in the low humidity experienced (building air conditioning plants will cool air below the target and then warm it back up to ensure it isn't too humid). I'm guessing the 787 cabin compressors don't heat the air so much, so perhaps lose less moisture this way? But I can't imagine them carrying a tank of water to actively humidify the air?

You're correct with regards to the Dreamliner but there has been at least one rather thorough independent test of air quality and relative humidity performed by Carlo Giaconia using an A319 flying a variety of short haul routes. His paper is here.

787s have humidifiers for flight deck and crew rest air. Something like that is being done on the A350 and 777X as well, with humidification of first and business as on option. For the most part, the cabin experience is the same.
The colder the air, the less moisture it can hold, so if you cool air with nonzero relative humidity, the resulting air will have a higher relative humidity, which is why air conditioners have dehumidifiers. If you warm air, the result has a lower relative humidity. If the air outside is -40, heating it to room temperature is going to create a very dry environment that sucks the water out of you. This has nothing to do with bleed air or electrically heated.

There's also the claim when the 380 and 787 were entering service that they're pressurized to 6000 feet, while previous gen ac are pressurized to 8000. I'll leave it to someone else to say how often their Cabin Alt climbs to 8000.

Hasn't the claim been the humidity could be set higher because of the CFRP fuselage? Like less corrosion risk or similar?

Given the issues with the Trent I'm surprised this has not caused more of a stir.

Was this a mechanical failure of the engine, a precautionary shutdown, or was there an external cause?

Perhaps it was an ingested small UAS (aka drone) so a drone strike/mid-air collision, not a bird strike.

It's not 'set' higher - as Dinger noted there simply isn't much moisture in the outside air at 35k - compressing it and heating it doesn't change that regardless of how you do it.
What they were able to do on the 787 - that hadn't been done previously - was have humidifiers to improve the humidity of the passenger (and crew) air. The carbon fiber construction meant there is no corrosion risk associated with that, but the ability to add humidifiers for passenger comfort has always been there - just seldom used.
It's up to the operator as to if they bother to service the humidifiers with water between flights...

BTW, for all the problems the Trent 1000 has been having, the current generation of engines is still an order of magnitude more reliable than what was available 40 years ago. Back then, people thought a shutdown every 10,000 hours was just fine, today a shutdown every 100,000 hours is cause for concern.

787 Humidity
 

Zonal driers in the crown area stops the moisture from condensing out, it is then recirculated back into the cabin to keep the humidity level above 15%.

At least, thats the theory.

Back to exploding engines....

6000 foot cabin at what cruising altitude in a B787?

I think people are getting caught up in Boeing spin here, our 30 year old 757s regularly cruise along at 6000 feet cabin altitude but our 737s sit at 8000 at the same level. Both use standard engine bleed as far as I'm aware

Once again association does not equal causation.

Big pieces typically equate to loose larger bits which often stem from the cooler parts in a turbine. I was under the impression that the earlier publizied problem was in the hot part of the turbine.So I remain neutral in picking a cause out of a news item.

I'm surprised how little factual information has been released about this incident, especially given the history of problems with the Trent on the 787. The only photo of the affected engine I could find had a large advertising board placed in front of it to try to prevent photos of the damage. Normally, by this stage, we would have seen photos of the damaged engine, know the variant of the engine, the number of cycles and hours it had done, and have some idea about what part of the engine had failed, even if the cause is still to be determined.

Twitter had this amusing observation;