There is no “standard” (except for ACX audiobooks).
Most of the “quality” comes from the quality of the recording and the performance. That includes a good microphone and a good room (either a “dead” soundproof studio or a music hall with “good acoustics”). It’s not easy to get a good acoustic piano recording at home. 
… Or any acoustic instrument, really.
There is The Loudness War where everybody tries to be louder than everybody else. 
That makes everything constantly-loud, killing the dynamic contrast and making music boring!
Radio stations use compression and limiting to make everything “loud” and the same volume, and they try to be louder than the other stations.
All of the popular streaming services use loudness normalization (different from regular peak normalization) so there isn’t much variation between different recordings. They mostly do this by lowering the volume of the louder tracks. Some quiet sounding tracks still can’t hit the target volume without clipping and they will remain below the target. The streaming services don’t use compression/limiting so unlike broadcast radio they aren’t altering the “performance”.
Your normalization step will set the peaks to exactly -2dB. You can set it to 0dB to make it 2dB louder. …Nothing bad happens when you get close to 0dB but you can get clipping (distortion) if you go over. That’s the highest peak(s) in the file and it’s possible that there is only one quick-short peak at that level. Regular normalization is a simple-linear volume adjustment and it doesn’t affect sound character-quality unless you go into clipping.
Note that peaks don’t correlate well with loudness. Almost all commercial recordings are compressed or limited (limiting is a fast-kind of dynamic compression) to bring-up the overall loudness without boosting/clipping the peaks.
Compression changes the dynamics (the relationship between loud and quiet parts) so it’s creative-judgement call. If overdone it can mess-up the sound.
In general, a solo acoustic recording won’t be as loud as a more “dense” recording of a full band, etc.
If your radio preset isn’t getting it loud enough try the legacy limiter (with make-up gain). Effects → Legacy → Legacy Limiter. Maybe start with a limit of -6dB and you can experiment from there.
Also note that anything that boosts the volume will bring-up the background noise making it more noticeable.
…Most of us don’t have the skills (or tools) of a professional mastering engineer and we can’t get the same loudness with as little damage. But if you have a good stereo with enough analog power & gain, you can simply turn-up the playback volume. 