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Every site and AI and Google say that one way of measuring a galaxy's diameter is in terms of its isophotal diameter, using the blue D25 standard, using units of, "25 mag per arcsec2".

But magnitude in astrophysics is a relative standard, so to speak, so...

How much brightness is '25 magnitudes'?

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    $\begingroup$ Magnitude is not relative $\endgroup$
    – planetmaker
    Commented Sep 12 at 5:09

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The D25 diameter is defined in terms of the diameter of a certain isophote: specifically, as you note, the isophote where the $B$-magnitude surface brightness has a value of 25 mag arcsec$^{-2}$.

The system traditionally used for this is the standard Johnson $B$-band, where the magnitude $m$ is defined as

$m = -2.5 \log_{10} (F_{\rm object} / F_{0})$

where $F_{\rm object}$ is the flux of the object and $F_{0}$ is the reference flux; in origin, this is the flux from the star Vega observed with the $B$ filter. I believe this is usually defined as $F_{0} = 4260$ Janskys (Jy).

So, working out the math, $m_{B} = 25$ corresponds to a flux of $4.26 \times 10^{-7}$ Jy.

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