Because they're active, as a result of the ANC function, just about anything will go loud through them. You can plug them into a good source, and they'll do a good job at preserving it.
Since you mention Tidal from your phone, don't rule out bluetoothing direct, and enjoy no wires. Again - try without preconceptions if you can...
The wonder of the things is that just about everything sounds great through them, sharp without ever sounding harsh, smooth without sounding fuzzy. Might remind you of your speakers...
I have had HD600s for 2 decades, and Oppo PM-3s more recently. I use these Sonys in preference to either. The fact that you've got in-built noise cancellation (which you can turn off) along with EQ, and also a sound position tool in the app on the phone, means you can put the sound out in front of you at the click of a button, if you don't like the 'between the ears' effect headphones have.
If you're also half-considering IEMs, however, I have one more suggestion: Etymotic ER4. You must get the things deep in your ear canal and you therefore need to sort out whether the silicone or foam tips suit you best because they're lousy if they're not well inserted and sealed. After much experimentation, I use the Comply precision tips. However, when you get it right, they're like plugging the music direct into your brain. Get it right and they'll make listening to the Kiis sound like you're listening through a duvet, without sounding in any way bright. Oh, and these blighters really do need a very good source to shine - they don't much like Apple phones or iPods. I use mine with a Sony NW-ZX2 on the move, and occasionally a Linn Akurate DSM/3 at home.
I also have ER4s, SE535s, HD600s, and B&W P7s. For me the SE846s top the lot. Plus will make the most of any source.
For IEMs, discomfort over time, ease of inserting correctly, fit and seal, and ear wax are all common objections. I have had a few pairs of IEM and have experienced all the above. but the SE864s, once fitted with custom moulded gloves took all of those away. It's about the fit and seal to get these things singing. Not a close enough fit, they are uncomfortable and SQ is compromised through 'frequency leakage'. Too close a fit and they are plain uncomfortable for any time. I got custom ear gloves from Ultimate Hearing Protection Systems. You supply (local audiologist) an ear impression, then they make custom fit for your ear. They specialise in Shure and cost was £120 for what has been a totally transformed experience in both fidelity and comfort over time, plus ease of insertion. MIndblowing.
Mix and match hardware for the headphones in my armoury is, MF Xcans (retired), FiiO E17 dac headphone amp,
FiiO Mont BLanc for IEMs, Sony NWz A15 Walkman (native FLAC support, great internal dac), iPhones/pads, Moto g6,
And in main system I have Benchmark dac2 HDR - Pre amp/dac which is also a headphone amp.
At home, Listening to FLACs either on my network or streamed from Qubuz, the SE846s straight into the DAC2 HDR is the most stunning sound.
On the go, the Sony NW/Fiio and SE846 combo is tops.
iPhone 7 qubuz app FLACs into SE846s is next best. That's without any external dac btw.
SEs and Apple are more than capable of making the most out of Spotty 320k streams, YouTube etc. Nothing to be sniffy about there - easy, uncomplicated, pocketable.
I barely use the HD600s, and for my over ear fun, I really enjoy the B&W P7s. Unlike the senns, they have a very easy in house sound, erring on the smooth, but fun and very pleasing for most rock/pop/folk. The wireless BT is also great. I couldn't wear them walking down the street (that goes for any over-ears) but they are great for travelling, although i left the first on an aircraft seat - never to be seen again..
I may look at a portable amp dac for Apple with BT, but cannot be bothered with CCKcamera connection kit.
I would ditch all the others for the Shure 846 IEMs if I had to make a Sophie's Choice. Only with custom mounds is the caveat.