You can dip your giant robots into an electrolysis bath after taking on invaders from another dimension a la neon genesis evangelion.

I'd also assume it'd be useful for repair of critical components that undergo trauma. Such as bridges, and buildings that might be struck by vehicles, or repairing prosthetics and other things that can be damaged at the same time as the human they're attached to.

You'd need to make your bridges out of this fancy metal foam instead of boring old (read: "cheap") hot rolled I beams. That would be a massive technical challenge. It's theoretically possible but would require new construction techniques. At the very least we'd need to figure out a new way to protect it from the elements that doesn't negate the self healing properties (this foam doesn't look closed cell, hello corrosion) Probably expensive beyond all practicality.

Furthermore, vehicles basically just bounce off the structural elements of bridges and other structures like that. It's not really a problem.

If anything we'll see this kind of stuff used in expensive niche applications. Low volume bespoke electronics in high vibration environments would benefit from being able to "heal" like this. I can also see it being useful when applied as a coating that protects the material underneath, basically a self touching up paint job (like galvanizing, but possibly with a wider array of materials than just zinc). This could be very useful for items in corrosive environments.

This is mostly useful to repair expensive and customized things like prosthetics. The other examples would just get the parts replaced as they're not customized.