For protection a piece of stainless steel, can use paints, modeling clay, silicone, or liquid glass - materials that will also keep things hidden from prying eyes.
I'd get very curious if I find a steel washer inside a blob of glass. I checked the melting points, and they're quite close together. As much as I like the corrosion resistance of glass, this isn't very practical.
Melting point of stainless steel - 1300-1500°C
The melting point of liquid glass - above 1000°C
Temperature during a fire - 1000-1350°C
Well, unless you happen to live right next to the vent of an active volcano (where, incidentally, the maximum possible temperature of magma is up to 1700 °C), I don’t think your stainless steel plate is going to melt and fuse with molten liquid glass (the glass would melt long before that). It seems highly unlikely that stainless steel would melt in a typical fire (though whether any engraved text would remain legible is a question for a separate experiment). If, however, you were to intentionally subject the plate to extreme heat, that would be an entirely different matter.
I think m2017 doesn't speak of molten glass but of "waterglass" which is
Sodium silicate, a water soluble silicate compound (mostly Sodium based but other alkali metals work too) which can be used for coatings and other use cases. In liquid form it can react with carbon dioxide to harden permanently to insoluble silicic acid.
Yes, you’re right. Thanks for the clarification.
I wouldn't consider such "coating" as very resistant to all kinds of harsh environment for stainless steel.
On the other hand, it should provide protection against non-aggressive environmental factors, such as exposure to air, water, or salts (chloride ions from table salt can cause pitting and crevice corrosion in stainless steel, so don’t keep your inox washers in the kitchen

), in short, things commonly encountered in everyday life.
I wouldn't want to expose my metal washers with my mnemonic words to anything harsh.
And who’s going to ask you about it?

In such cases, a hostile environment finds its own "victim".
Can you do something similar for stainless steel razor blades?
PS
Razor blades are temporary solution, since they have only thin stainless layer.
What’s coming up next? Engraving on a needle?

If corrosion is a problem, I would suggest titanium washer as alternative option.
Why bother with small change? Go straight for gold washers, since it’s the most inert (corrosion is no match for it) metal, and buying it is an investment in itself.
True Casascius coins were supposed to feature an engraved seed-phrase; but not something to be applied as a sticker.