Is HeraldHenry Really 128?

Did they implement this?
See this and the accompanying official forums' official post.
FFXI Herald Henry
Official Forum Post

You mean that post from 2013? I'm sure /something/ has had to have changed in the last 7 years, but I'm not going through version update notes to look it up for you. Maybe someone else will recall when/if this was ever addressed.

Pretty sure it's still capped at your level, so at that point they may have planned to continue increasing ilevel, but then they stuck us at 119.

If this isn't known/proven, it'd be pretty easy to check by calling a 119 pet at 99 then again at 119.

I am thinking that even though your gear now adays states that it is indeed 119, the stats you can equip goes beyond that. This is talking generally about all content. How else can a party of 6 take on bosses that have an ilevel of 150 in Reisemjima?
Anyway back to the topic in question I would guess the cap for your pet would stay at 119 too. Only way to make your pet stronger is to equip other gear unless they make a weapon for your main hand that's 128?

Bst jug pets have never legitimately been able to increase above the master's level.

I remember there was a case when Lucky Lulush was new, that it could get to level 101 or 102 under certain circumstances. However, they patched that rather quickly.

The cap specified in those posts is about how high it *could* reach if master ilvl could reach that high. it is the stat that is specific to the weapon so to speak. The ACTUAL level of the pet depends on the circumstances when it is called. The caps are only about potential.

So if they increased the ilvl more, several current pets would fall behind but some would continue to scale upward.

The item level system is a mess and practically abandoned for the most part. They stopped raising it before they added the wildly varying augments of Reisenjima gear.

The reason was because your average item level is the level of your trusts and they didn't want trusts to be higher level than 119 at the time. And after adding augmented gear, I'm sure they gave up on even trying to backtrack that.