I have used the TVS and schottky in series (pointing opposite way), for higher turn-off voltage in the coil. No obvious problems after it was appropriately sized. The catch is that the power dissipation in the TVS is higher in proportion to its voltage drop. With rapid cycling, the package size that worked for the schottky can turn into a smoky surprise.

Not sure if this way of faster turn-off would be important for a relay, maybe better achieved with a SSR? I found it useful for a solenoid that produces some mechanical action. The advantage of a TVS (avalanche diode) vs a zener, I'm not sure. In principle it is an opportunity to reuse a part that is likely already part of your world if you are doing, e.g. 24V systems, but the power dissipation needs may be higher (depends).

@Pete W‭ Yeah indeed, I'll already have some 33V TVS elsewhere in the BOM. As for replacing the relay, indeed some manner of SSR-like solution is preferable (faster, cheaper, more reliable). There's various "smart high side drivers" that are very good for this and they can also drive analog signals. Though if you use such for driving a solenoid, you are going to need a flyback diode for the solenoid anyway.