I made a mistake telling you the relation should be from C to B. Instead it should be from B to C.
Well, following your simplified version, you would be able to create a template column in table B that contains the signed in user’s email, the item, and the words ‘NOT USED’. A similar template would be created in table C. There you would already have an email column, item column, and status column, so your template would combine all three. Then you can create a relation in table B that joins the template in table B to the template in table C.
To enhance that for your ‘not so simplified’ version, you could create another template in table B that only joins the signed in user’s email and the words ‘NOT USED’. You would then create a similar template in table C. Then you would create a relation that joins that template in table B to the template in table C.
So simply adding a condition that checks if the first relation is empty would tell you if that particular item has been claimed and unused by the user. The second relation could be used with a rollup column to count the number of unused items a user has (assuming that a user can have up to 4 unique items at one time.)
In the end you can then add a visibility condition on your button to check if Relation1 is empty Rollup is < 4.
Edit: If count is not important and a user can only have one item at a time, a simpler alternative to the above would be to create a relation in Table A that links the user email to the email in Table C. Then you only need a Joined List column to create a string of all the Used/NotUsed statuses. Finally you could create an IF column in table A that would check if the Joined List column ‘includes’ ‘NOT USED’ or 'NOT USED ‘is included in’ the Joined List column. That could be your boolean result by returning ‘true’ or ‘false’ for the result in the IF column.
Kind of several ways to handle it. You could also do the simple version in Table B too, by creating a template with the signed in user’s email, and create a similar relation/joined list/If combination.