Q: about 'barre' in guitar 5-stave & TAB notation

From the guitarist's perspective, would it be more clear for chords which (optimally) use a barre, to have the barre explicitly added to what is seen here?

Regarding TAB, if the TAB staff shows a chord with the same fret number on multiple strings, then it's a good chance that a barre is involved. Nevertheless, the barre can be entered onto tablature as "C" with the fret number as Roman numeral.
Regarding standard notation (and TAB), see:
https://en.wikipedia.org/wiki/Barre_chord#Notation
for info. on notation of the barre technique with regards to customary editorial styles.

I recognize F & F# are an "E-form chord", but essentially barred at the 1st or 2nd fret. Likewise, the Bb & B are an "A-form chord" also barred at frets 1 or 2.

The following image shows that a barre can be placed on the fret-board diagrams (not that you intend to use).

Also...
That image shows an important distinction how to "spell" chords in standard notation.
As you are aware, F & F# are an "E-form chord". The chord shape is the same - that barred F chord "slides" one fret higher, thereby sounding all chord tones sharp.
Okay, so here's what's important: There is no B♭ in an F♯ major chord. (The F major chord is based on an F-A-C triad. When F gets sharped, A gets sharped.)
Look at the image to see your notation on the first line compared to the second line. For example, look at the arrangement of the noteheads of the B♭ chord compared to the B chord. The arrangement (and note-spelling) consistency displayed on the second staff aids readability. The noteheads are nicely stacked.
Your G# chord almost reads like some kind of a C chord (ignoring the accidentals).