Simeras

It's probably the DSP. It can do it's magic given a digital signal, while being bypassed (on most BT headphones, so you could still use them with a dead battery) with an analog signal.

It is a good price for an authentic one. So be sure to check.

If audio input is analog, then there can be differences depending on source. If input is digital (Bluetooth, Wireless dongle), then they will sound the same on any platform.

Sennheiser TWS3 has/had issues with bud not charging in the case. Mine has no issues so far (1 year of use), but I know someone who had to RMA his. And there are threads about it.

There is nothing magic about amps. Get one that will have enough power and you're set.

Which ones? TWS3 are great. But if they don't seal well, ANC and overall sound will suck, of course.

They can be a bit finicky to fit properly though. But that depends from ear to ear.

These options depend, and are limited, by the firmware of the headphone. You cannot just save whatever preset with a 3rd party EQ.

K3 will have more than enough power to drive HD560s with single ended output (3.5mm jack). You don't need anything else.

Try non-gaming headphones with big earcups. Try IEMs.

This post will probably get removed, as you can't actually ask advice in this subreddit...

Do you have local audio stores where you can go and test various IEMs? I would strongly recommend that, instead of asking opinions.

I replaced SE215 recently, and all IEM's I've tried sounded drastically different. So best to listen before you buy.

You are unlucky.

More neutral sounding ones would be AKG K371.

I would assume they are tested with HATS at some point in development/QC. I would also assume, even french HATS do not have a wig of wonderful hair.

So no, not suction. Closed back headphones usually have some vent holes (ports), they are not totally sealed.