Short answer: you can't safely inject standard two-part spray foam into a closed wall cavity. It expands hard and fast, and forcing it into a sealed cavity can bow drywall or crack studs. The foam you see sprayed on open framing is not the same as an injectable product - and confusing the two leads to damage.
Why not
Expanding spray foam needs room to rise. In a closed cavity it has nowhere to go but out - against your drywall. Injection/pour-in-place foams are different, lower-expansion products for closed cavities, and even those need care.
The real options for existing walls
- Exterior re-clad: add exterior spray foam or rigid when the siding comes off.
- Open the wall: during a renovation, spray the open framing properly.
- Blown-in for closed cavities: a dense-pack cellulose or fibreglass may be the practical retrofit where you can't open the wall.
An honest installer will tell you which fits rather than injecting foam that damages the wall. See wall insulation. Get a quote.