Sound power and pressure level, what's the use?

The sound power level indicates the total acoustic energy that a machine, or piece of equipment, radiates to its environment. The sound pressure level is a measure for the effect of the energy of an acoustic source (or a collection of sources) and depends on the distance to the source(s) and acoustic properties of the surroundings of the source.
Given a well defined operation condition, the sound power level of a machine is a fixed value, were the sound pressure level always depends on position and environment.
In relation to the Machinery directive we speak about the "emission sound pressure level". This represents the sound pressure level an operator or bystander is exposed to, in a free field above a reflecting plane.

SPL, SWL, LpA, LwA

The definition of SWL? What about:Safe Working Load, or Static Water Level
SPL is widely used for "sound pressure level", but these characters could as well describe "sound power level" although a few decades ago sound power level was abbreviated in the US with PWL.
Even a wikipedia page refers to SPL and SWL as being valid descriptors. Bad habits exist, and wikipedia apparently is not always correct. SPL and SWL, widely used in relation to sound, are confusing and not the correct ones to use for this purpose.

SI ( International System of Units) only contains units for pressure and power, not for levels.
Levels are described in ISO standards, using the following abbreviations or descriptors:

L_p: sound pressure level, and
L_W: sound power level

If A-weighting has been applied, then the descriptors above contain the character A at the end, for example: L_pA

dB and dB(A)

dB (abbreviation for decibel) is the "unit" for both pressure and power level. It's not a unit because it's the logarithm of a quotient, that's why L_p and L_W are both expressed in dB, each with a different reference.
The decibel is essentially unit-less!
The A in dB(A) is not supported by ISO standards. The reason is that the A must be contained in L_pA or L_WA, and with a proper description. That what's needed for a good specification, requirement or measurement result.

If you see db, DB or Db in relation to noise or sound levels, the whole message is suspicious because if someone does not even know that dB must be used (e.g. knows were dB "comes from"), the person, institute or company will probably lack the most basic knowledge about sound levels and related subjects.