Apple Soundcheck is rubbish.

Note the songs with reduced volume and give the playback volume adjustment a tweek in the info panel, it's under options when doing a song info check. Other than that you'll need a computer and a sound editor of your choosing to batch adjust everything. (The assumption is that your iPad may be older and lower specified as it's a shop one and will not work well with a stand alone app and a load of songs to adjust).

Sounds like the song files are set at different volumes. Is there a spotify/apple music/music streaming service of choice you can use?

What Sandwich said.

Even streaming will have tracks at different relative loudness. reminded of this in the car yesterday. Volume up to be able to hear more of ‘one of our submarines’. Some complaints when ‘Last’ burst out of the stereo with a bit more oomph immediately afterwards. The dangers of shuffle.

What files are you playing?

You might need to add normalisation to the files.

I used to use DBPoweramp which worked really well.

From memory your need to use it to add a ReplayGain tag to your music files. You could run a process that will do the whole library in one go.

Although I have no idea if Apple uses ReplayGain or if you need to do it a different way, but the theory is the same.

Edit: Apparently the ReplayGain plug in will also add ITUNNMORM tags which is probably what you need.

I dug out an old iPad 2 and even though it's clunky it plays all the songs at the same level.

I dug out an old iPad 2 and even though it’s clunky it plays all the songs at the same level

That’s interesting. None of mine do. And nor do my iPods. What audio settings are you using on it? What kind of audio files (CD rips, iTunes/Apple Music downloads)? While I expect some differences between track volumes, some are more dramatic than I’d like.

dbPowerAmp! I remember that.

Not having the issue on your iPad 2 suggests that you have noice protection settings enabled on your other device, ipad 2 iOS didn’t have the sound protection.

https://discussions.apple.com/thread/252120207

Never bothered with sound check, I expect different albums to be at different levels of perceived ’loudness’, due to mastering levels - look up ‘loudness wars’, where compression was applied to recordings to increase the apparent loudness of recordings when played on the radio. I’m perfectly capable of turning things up and down as and when necessary, especially if I’m playing classical or acoustic music, where a wide dynamic range is a crucial part of what the music is about.

https://dynamicrangeday.co.uk/about/

https://en.wikipedia.org/wiki/Loudness_war

I sold hifi as a Saturday job back in the 80’s, and I used to demo different systems to people coming in to replace existing audio equipment, often cheap cardboard Amstrad tower systems, and one disc I used to play was a Rachmaninov piece which had a nice soothing section, which then suddenly had several loud bits, and inevitably the customers would jump!
And they would always go away with new kit, a couple of times customers came back to personally thank me for giving me so much pleasure from listening to music that had been transformed. Nobody ever complained about loud bits and quiet bits being too loud or too quiet.

We are listening via Apple Music if that helps.

Thread ressurection.
This works. He later on sets the volume at 100% ,which is what I've done.
Didn't work on my old android but does on our 6S.
https://discussions.apple.com/thread/252302664