Shift-selections only select staff-attached objects, and chord symbols are treated as system-attached objects (like tempo markings and system text). You should find that Select More works on chord symbols, and there’s some undocumented behaviour here too: if you select the first chord symbol, then Cmd/Ctrl-click the last chord symbol you want to copy, then type Cmd/Ctrl-Shift-A it should select all the chord symbols in between (as opposed to the usual Select More behaviour, which is objects of that type within that bar, then system, then flow).