What JSON is
JSON is a text format for nested data: objects with named keys, arrays, strings, numbers, booleans and null. It has no date type and no comments.
Every web API, most configuration files and anything that talks to JavaScript.
What BBCode is
BBCode uses square-bracket tags. Table support is not universal, but table, tr, th and td are widely implemented.
phpBB, vBulletin and forum software descended from them.
What changes when you convert JSON to BBCode
Four shapes all read correctly: an array of objects, an array of arrays with a header row, an object of column arrays, and an object keyed by row id. A single wrapper key holding the array, which is how most APIs reply, is unwrapped automatically. Nested objects are flattened one level into dotted keys; anything deeper is kept as JSON text in the cell, because a table cannot hold a tree.
Check that your forum has table tags enabled. Many boards ship with them switched off.
What carries over from JSON to BBCode
JSON records 5 things about a table that BBCode has no way to hold.
JSON distinguishes a number from the text of a number; BBCode does not, so every value arrives as text and has to be re-parsed by whatever reads it next.
An empty cell and a missing one are the same thing in BBCode, so a null and an empty string in the JSON both come out blank and can no longer be told apart.
JSON can hold a value that is itself a list or an object. BBCode has only flat cells, so nested values are flattened into one cell rather than being spread across columns.
A line break inside a cell ends the row in BBCode, so line breaks are replaced rather than carried through.
The keys stop being repeated: BBCode writes the column names once at the top, so the same table takes noticeably less space.
BBCode is the end of the line for this data. Reading the table back out of it is a separate and much harder problem than writing it, so keep the JSON if you will need the values again.
The identifier 007 comes out of the BBCode as 007. Reading it as a number would have made it 7, and an id that changes value is worse than one that stays text.
The role "Analyst, data" survives with its comma, in one cell rather than split across two. That is the first thing to check in any converted table, and the usual place a BBCode file goes wrong.
The quotes around Jonah "Jo" Pryce are left as a plain quote character in the BBCode.