There is no actual “standard” because "loudness is subjective (consider an elderly person that has reduced hearing for high frequencies - a fairly “quiet” low frequency sound may sound “louder” than a “loud” high frequency sound). “Loudness” is actually very complicated because there are many factors affecting how we perceive it (Loudness - Wikipedia). There is however EBU R128 which is a “recommendation” rather than a “standard”. EBU R128 is available here (PDF) https://tech.ebu.ch/docs/r/r128.pdf
The simplest approach is to use the same RMS level. This is a kind of “average” level (Root mean square - Wikipedia)
The RMS level is a much better approximation of loudness, though it takes no account of hearing being more sensitive to some frequencies than others (Equal-loudness contour - Wikipedia). it is however a measurable and verifiable scientific measurement. There is a plug-in available for Audacity that can “normalize” to a specified RMS level: RMS Normalize
A more elaborate approach is this plug-in, based on the ReplayGain algorithm. ReplayGain plug-in
The “New Version” allows you to amplify to a specified “loudness” level.
There is also a 3rd party application called “Wave Gain” RareWares - Other audio tools and formats
The second link is a version that is optimised for recent versions of Windows and is marked “Download (135kB)”.
I’ve not tried this myself.
There is also a very good free audio player called Foobar2000.https://www.foobar2000.org/
This has “equal loudness normalizing”, though I’m not sure if the normalizing can be applied to WAV files.