For Delta IV Heavy, according to Spaceflight101:
The CBCs functioning as boosters are attached to the central core using thrust struts that interface with the interstage section of the launcher to transfer loads from the boosters to the rest of the vehicle. Additional attachment points reside in the base of the vehicle right above the engine heat shields.
The "thrust struts" described are the thin horizontal pieces near the top of the boosters. The "additional attachment points" are at the bottom of the cylindrical portion of the cores, just above the tapered boat-tail heat shields around the engines. This diagram gives a slightly better view of the latter:

All the force differential between the boosters and center core goes through those attachment points.
For Falcon Heavy, the setup is similar:
The boosters are attached to the central core stage via structural interfaces in the aft section and interfaces that connect the upper portion of the boosters to the interstage area of the Falcon Heavy via thrust struts to transfer loads to the vehicle. Separation of the boosters is accomplished using collets in the structural interfaces, avoiding the use of pyrotechnics since SpaceX prefers to use systems that can be tested and re-used. The reaction control system of the boosters ensures a clean separation from the core stage.
The base connection points appear to be singular, rather than dual as on the D4H:

The struts are pretty substantial; from the first picture in the question, I estimate the height of the upper struts to be about 24cm.
For Soyuz, the force seems to all be transmitted to sockets near the top of the core stage which are engaged by the nose of the boosters; I believe the straps at the base hold the boosters in position without transmitting significant load.