That addresses individual equipment grounds and bonding jumpers, but doesn't explicitly address establishing a grounding path for a ground bar. It definitely wouldn't apply to a current carrying neutral bus bar, in my opinion.
I've seen a wide range of interpretation of this by inspectors over the past few years.
Screws into enclosure are only for gnd bars, no neutral bars.
Listed accessory ground bars from a mfr typically rely on two fasteners to mechanically secure and bond it to the already grounded enclosure. The instructions for installation require nothing further. If you want to add an additional jumper between bars there shouldn't be an issue. I would at least use the min size required for that service/feeder egc. And its purpose is for gnds only.
A neutral bar is sold as a different part # for a different purpose. I would think a ground bar used as a neutral bar could fail inspection as it is being used for a different purpose. (No I don't have the listing details for either.)
If there was a second neutral bar
field installed (and not excluded in mfr instructions), I would think the same conductor supplying neutral to the panel would be required to jump between neutral bars unless the mfr supplies a jumper. Anything less alters the mfr's rating of the neutral bar "system".
I have yet to ever add a second neutral bar to a panel. Only replaced one, once.