Best way to tighten up these chairs?

Daughter’s school chairs are all pretty wobbly. They’ve been patched with dowels here and there in the past and have also had the diagonal screw added.

What would be the most conical way of tightening these up?

My thoughts are:

1 Loosen the pocket screws up, hit the joints with glue and a compressor and clamp.

2 Replace the diagonal screw with a threaded insert and bolt

I’m far from an expert on any of this so I’d love some advice. I haven’t committed to helping at this point, just aware of the problem and wanted to take a look.