Crampons and Ice Axes
When the snow turns firm and the slope steep, it's best to break out to the pointy end of the gear to ensure sufficient grip and confidence.
One of the more underrated and arguably necessary pieces of pointy-ended gear are ski/splitboard crampons. These crampons are binding specific, as the crampon attachment point is particular to the binding crampon interface. The crampon pivots underneath your boot as you tour, and the crampon teeth bite into the firm snow providing purchase when skinning. It's certainly worth carrying a set with you for any late winter / spring touring you'll be doing.
If you intend to exercise your inner-alpinist through couloir bootpacking, ridgeline traversing or scrambling, then there's good reason to carry boot crampons in the pack. Ski boots should be paired with step-in / automatic crampons, as these will provide the most secure fit due to the way the crampon toe and heel bails attach to the toe and heel welts of the boot. For technical hiking boots without toe and heel welts, you'll want to use a semi-automatic crampon. For Dynafit boots like the TLT8 and Hoji Pro Tour / Hoji PX, you'll want to use the Cramp-in Crampon.
Aluminum boot crampons are ideal for general purpose mountaineering. For more durability and purchase power, it may make sense to upgrade to a crampon with steel toe points. If you're seeking utmost durability and strength, then consider a full stainless steel crampon.
If these pointy things aren't enough point for you, then going with a whippet(s) or ice axe or combo is the next step. Whippets allow for the quick addition / removal of a steel pick to the top of a touring pole, providing purchase when boot packing, and increasing your chances for self-arrest if a fall should occur. Ice axes are stronger and burlier, and can be stored on your pack when not in use.