S-meters are nothing else but power (input) meters.

Amateurs and meter manufacturers long ago learned, that when giving signal
strength reports, it is more convenient to refer to meter indications in
terms of S-units rather than micro-watts or nano-watts.

At HF, when the meter reads S-9 the power entering the receiver is 50
pico-watts. There's a slight complication above S-9 when the meter scale
changes to decibels above S-9.

When the reading is S-9 plus 40 dB the meter is actually indicating about
S-16. It's just a matter of scale graduations and printing.

The S-meter does NOT measure or even indicate field strength. It indicates
nothing except that an increase in meter reading corresponds to an increase
in field strength. Which may be nice to know but by how much of an increase
is anybody's guess.

Measured field strength depends on the type of antenna, its efficiency,
ground losses, etc. It is possible, of course, to calculate field strength
in the vicinity of the antenna from S-meter readings provided the antenna,
its directivity, transmission line, tuner and ground characteristics are all
known numerically. Which in the amateur situation they are seldom not! Or
even in the professional situation.

You've all got one. To repeat - the S-meter is a power (input) meter.
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Reg, G4FGQ