Hi Max -
I use my iPhone with Shure earbuds a ton while travelling (on planes and, when I was in Germany over the fall and winter, trains) and falling asleep (mainly in hotels on the road but also if restless or fretting at home). I have a small USB DAC that plugs into the phone, but I don’t always / often use it unless I’m not falling asleep to an audiobook. I used it with on-ear Sennheisers to good effect, as the native iPhone out wasn’t very good with those. I have lossless Tidal downloaded (over wifi) loaded up for the trip, and play via the Tidal app. I find battery life not affected by playing music as long as you don’t insist on having the screen glowing while you’re listening. More noticeable if it’s powering the DAC but not bad actually. I have an old iPhone 6; it’s (still) my first iPhone, so a bit long in the tooth. I started on a collection of progressively newer and better iPods, ending with whatever the last thin and beautiful one was... iPod Touch 5 maybe? It likely had the best internal DAC, or at least the best native sound. Better earbuds can take you a long way, in my experience.... but I’ve not really had much above the Shure 215 series or equivalents, as I often sleep on them and the zero profile is good for that. They are not so expensive that I’d be devastated to have them stop working or, not to jinx myself by saying it I hope, if I misplaced them. My DAC is a small thing the size of a USB memory key (as is the Dragonfly) but saves space by not having the actual USB connector, using a short cord. Still, I find it a hassle and the larger outboard amp/DAC boxes hold no appeal as I’m often jamming crap in my jeans pockets to exit a plane with my carry on... not your use case, I guess. But still, my next move is just to buy the Apple Lightning to 3.5 mini jack cable that comes with iPhones 7 and newer; it gets good reviews (see Ken Rockwell heaping praise) and it’s as small and low power as it gets. Might be a useful investment of 10% of your budget to see how you get on before adding a box the same size again as your phone (which, for me, would mean shopping for a complete replacement player, in case that hasn’t come across already, haha. Or spring for the Dragonfly and give us a review of MQA on Tidal via your iPhone...
Best wishes with your search.
Regards alan