So your best bet is examining the attachment at the leg and table interface. It was 'strong' once...and could be made to be so again. Reinforcement inside the table could solve the problem. But as you only provided photos of the exterior hard to determine.

The fact that it's up against a wall...presumably 'permanently' you do have the option to attach the table itself to the wall. This would transfer some/most pushing force into the wall instead of the legs.

Reinforcing the legs could just require gussets. Imagine a flat piece of wood triangular shaped going from leg to table. This would allow the table to be used as normal and spread out the loads applied due to leverage.

For 'x bracing' you've got to make some decisions. You can 'box' the legs by using horizontal devices across the floor - but you already addressed this in another comment.

For decisions do you remain 'in tension' or attempt to solve both compression and tension? In tension means x bracing...which can be done with wire and/or flat metal strips. They'll resist pulling but not pressing thus requiring an X. They don't necessarily have to go all the way down either - but the height you're at any crossing elements will obstruct seated usage - and possibly seat storage. But wire cross bracing can be as simple as screw in eyelets and wire with wrapped ends - or as complex as wire rope with thimbles and wire rope clips.

If you can manage legs in the center across each long end that would also transfer the push/pull energy differently.

You could also criss cross from diagonal legs. It would make the underside look cluttered but would be less disruptive to seating and storage use - this still would require the wall side legs to be criss crossed laterally too.

The best solutions will involve forces being applied to screws in sheer and not tension. Depending on the leg material you could cross with strips of metal from bottom flat (underside) of leg to the opposite.

But seems like your wisest solution would be to replace the legs - which you're seemingly wanting to lean toward anyway.

Really this boils down to what you wish to spend and how aesthetic you want it to look.

You could also pocket hole screw holes into the legs and add hard wood 'washers' inside the table - going through the particle board and into the chunk of hardwood/washer (with glue) - but as I can't see the inside no way to see how easy/economical that would be.

Also - for whatever you choose to do...start with cardboard and fiddle with the shape referencing from leg to underside. Angles aren't impossible to work with...and the curved surface means either grinding/filing a convex for greater glue surface or going with attachments with less glue interfacing.