Really, it would depend on the stainless steel and heat treat. Painting with a broad stroke is a bad idea. There are carbon steels and tool steels that would also make bad choices for such tools, so simply saying "stainless steel is a bad choice" isn't useful or accurate.
Now, most of the tools I've seen for such things do not look to be quality that use stainless steels. In every scenario, I prefer to get regular tools and have them for my "oh shit kits."
Need a "survival shovel," get a good packable shovel. The cold steel shovels mentioned above are good and affordable.
Need a "survival axe," get a good axe of your preferred size. Fiskars is pretty decent, I like council tool's axes, knowing they'll need some edge work and a mask.
"Survival" tools are onky good if they're with you AND you know how to use them.
A good multitool like a leatherman or SAK is a good place to start. A lot of capability in a tool easy to have on you.
Next is going to be a packable shelter, either a tarp or poncho that be pitched like a tarp. You'll die from exposure before other things so getting shelter to extend your chances of surviving is a big deal. Consider some cordage to go with that tarp or poncho for the tarps I carry, I have the guylines already tied and a pre-fabricated ridgeline. I like the silnylon MEST from Etowah outfitters, packs quite small, is lightweight, and he includes everything needed to get it setup, last time I ordered one. I've mostly moved to ponchos though.
From there, it's figuring out how to get out of a survival situation and getting to safety. The goal is to get out of the situation, not stay in an emergency situation for extended periods. Compass, whistle, GPS, etc.
I should add, a 1st aid kit should probably be considered as well. Again, focus on what you can actually do. If you don't know how to use a chest seal, that's not top priority to include.
I'm not above having a cheat sheet or book along either as we can become idiots when stressed or freezing.