In the market for new headphones

These right here I'd say would do most of what you want (though they do not have transparency mode, like many of the ones that you don't want.

More info about said headphones can be found here:

https://amzn.to/3KgdWjF

Hi. Bose Quiet Comfort headphones can be wired or bluetooth, as you wish. They have the option of noise cancellation or can be switched to permit outside sound to be passed into the ear cups. They are comfortable, closed backed, and completely cover the ears. They have very good battery life per charge. They have quite nice high fidelity. They are not cheap.

The SteelSeries Arctus 9 is a great headset. It is cool because you can connect it to your computer through the wireless dongle then pair your phone to it through bluetooth and listen to both at the same time. Example, you're playing a game on your pc and want to listen to something on your phone. You can do that and you don't need a mixer to do it. The arctus also functions as a normal bluetooth headset, and if you need to use it as a regular wired headset you can do that as well and the cool part about that is you don't even have to power it on to use it with a patch cable. You can also use said patch cable to connect another device such as a victor reader or other device that uses a normal headphone jack to the arctus while you're connected to the pc and listen to both that way. Finally the coolest feature is if you're using it on a computer with the wireless dongle it shows up as two different audio outputs. Chat adnd game. You can send your stuff to the different outputs and control their volumes on the fly with the two volume wheels.

I'm going to post a couple of links to some headphones. All of these are technically Bluetooth, but like the subject line says, can be used with a wire as well. I think they will get plenty loud. The first is the Soundcore Life Q30 headphones. There is noise cancelling and ambient mode, both of which are very good for the price point. They can be used wired or wireless. I use these, and the sound quality is pretty good. It has a somewhat accessible Equalizer player in the Soundcore app. I believe battery life is up to 60 hours. https://www.amazon.com/Soundcore-Cancelling-Headphones-Comfortable-Bluetooth/dp/B08HMWZBXC/ref=sr_1_10_mod_primary_new?crid=3A5SMRIQTTPQD&keywords=soundcore+life&qid=1650991907&sbo=RZvfv%2F%2FHxDF%2BO5021pAnSA%3D%3D&sprefix=soundcore+life%2Caps%2C95&sr=8-10

The second link I was going to post do not appear to be in stock at Amazon sadly. If you can find the Status Audio BT-1, it is extremely comfortable, has about 25 hours of battery life, has an included cable to use wirelessly, and is an extremely comfortable pair of on-ear headphones. The only hesitancy I have in recommending this pair is that the build quality is a bit suspect. I've had mine about 8-9 months and they are still fine, but they do not feel premium in the hand.

Now we get to my daily pair that I use. While they do not have ambient mode or noise cancellation, the sound isolation is very good. You can also get up to 50 hours on a single charge. These are also extremely comfortable on-ear headphones. Also, they not only come with a wire to use them plugged in but also the wire has a microphone on there so if you want to use it with gaming or for talking you can do that. I also think that the music quality is excellent, and while they do not come with their own app or equalizer, there is nothing saying you can't use a third-party equalizer on your iPhone. I recommend the app called Boom 3D. Also, I guess you know already, but if you want to use them wired with your phone, you'll need to make sure you have a 3.5 to lightning adapter. Anyway, enough praise about the Soundmagic P23-BT. https://www.amazon.com/SoundMAGIC-Bluetooth-Headphones-Isolating-Headphone/dp/B097RF6YYF/ref=sr_1_6?crid=CRVN18OP30FS&keywords=soundmagic+p-23&qid=1650992512&sprefix=soundmagic+p-23%2Caps%2C86&sr=8-6

Hope this helps.