No worries :) Other than having an offical response, this may be an issue where you never get a satisfactory answer :). Best of luck anyway :)
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I tend to think of "binding" as being just the first step in spiritbonding. So, my opinion is that everyone is right who says that the two processes are connected, the word "binding" actually refers to the whole act of spiritbonding hence why it isn't labeled as "bound" after your first action in battle, but I think the OP has a point that there's a grammar issue there. Why not say "bonding" and then later switch to "bonded" once the gear piece has been completely spiritbonded instead of using the word bind at all. Though tbh I've never really taken much notice of it but I guess it would eliminate that confusion.
I'd like to chime in and say "Binding" has nothing to do with spiritbond. Bind and bond aren't the same word.
Bind Binding Bound. Bond Bonding Bonded.
To answer OP's question, I think it's intended to be "binding" like in the phrase "binding contract".
Items only become bound/binding to your character once the spiritbonding process has started. The words, as you say, may not mean the same thing. The process, however, is linked.
Binding, as in "binding contract", makes no sense what so ever sadly. You can not make a conscious agreement that can not be broken with an inanimate object, unless you were slightly barking mad yourself.
Fairly certain he just meant the use as a descriptor makes sense if you just take binding as an adjective (restricting) describing the type of gear as opposed to a verb/noun describing its spiritbond state.
binding adhesive
binding promise
binding handcuffs
etc.
ie -
binding as opposed to nonbinding/unrestricted
vs.
binding as opposed to bound in the sense of present and past participles describing its current stage of spiritbond.