Grid Fins are not used for air brakes.
Soyuz used grid fins for emergency stabilization. There is no such thing as grid fin airbrakes.
The grid fins passively stabilize the spacecraft while the LES is firing during an abort. They deploy by pivoting outward but aren’t otherwise movable.
In an abort situation, the booster may be in the process of tumbling or exploding or both when the spacecraft separates. Having draggy fins toward the back of the package quickly straightens out its flight. providing the maximum separation from the booster during the powered portion of the escape and allowing the fairing to separate cleanly from the spacecraft after the escape tower burns out.
Stable flight of a rocket requires that the center of aerodynamic pressure be behind the center of mass. The Soyuz LES abort has to carry both the orbital module (uncrewed during launch) and the reentry module (crewed) with it because the orbital module is stacked above the reentry module. The service module below that is left behind during an LES abort.
As for the Falcon 9.
No, NEVER. They are not designed with excessive drag. They are specifically designed to control the Falcon 9’s attitude. Pitch, Yaw & Roll.
Falcon 9’s first stage is equipped with hypersonic grid fins which manipulate the direction of the stage’s lift during reentry. The fins are placed in an X-wing configuration and are stowed on ascent and deployed during reentry.
In the atmosphere, RCS thrusters aren’t powerful enough to steer the rocket, and the engine isn’t ignited everytime. The body of the rocket can generate a little bit of lift when moving at the right angle, like a Soyuz. Grid fins are strong enough to resist to the hypersonic flow, that means the air goes by with a speed greater than Mach5 = 6150km/h or, for scientist, 1710m.s^-1. They can control the attitude of the Falcon even at high speeds.)
While the fins are relatively small – they measure just 4 feet by 5 feet (about 1m by 1.5m) – they can roll, pitch, and yaw the 14-story stage up to 20 degrees in order to target a precision landing.
Grids Fins acts like classic control surfaces we can find on an airplane. If they roll 2 by 2 in the same direction (“up - down” and “left- right”) they can control Yaw and Pitch. If you roll the 4 of them in the same direction, the Falcon9 has an excellent roll rate.
SpaceX grid fins are controlled by an open circle, that means that the liquid doesn’t come back in the tanks. During one of the firsts landings attempts, the hydraulic fluid was entirely used and the grids fins were stuck, causing the crash of the Falcon stage on the Droneship.
Theses Grid Fins need to withstand several types of airflow: hypersonic and supersonic, transonic and or course subsonic.
When going through a hypersonic flow, the air goes through the lattice at high speed and isn’t annoying at all because the shockwaves meet behind the fin.
Nevertheless, when going through transonic air stream, the air is going to bounce on the grids and generate a lot of drag and force on the fin. When going close to Mach 1, the Grid Fins aren’t really useful, because the shockwave is located before the grid fins, and no air stream through it equals stalling.
This applies directly to the R-77 as the missile should have zero issue in supersonic flight or demonstrate any issues maneuvering under increased physical vector quantities such those generated in high Mach launches in a dive etc.