... linear itself AND if we export the profile.

In most cases we want to save 8-bit image formats (here JPEG) as
non-linear, even though the work image may have been linear itself (yet
with higher bit depth). The reasons are shadow posterization on low bit
depth, and the fact that JPEG compression was designed for perceptually
uniform RGB and introduces shadow artifacts with linear RGB (see #1070,
message by Elle Stone). The only exception is when the creator was
working explicitly on 8-bit linear (not higher bit depth) AND if we
export the profile (otherwise most loaders around assume sRGB). In such
a case, let's consider the creator knows what one is doing and keep the
exported image linear.

Similar logics is already used in PNG exporter (though a bit of a
variant since PNG supports 16-bit so it is instead: 8-bit linear without
profile is promoted to 16-bit non-linear, and kept 8-bit linear with
profile).