De toute façon translates to anyway but that doesn’t mean tout means any. It still does mean a generic, singular all here (all outcomes = whatever the outcome = any outcome = every outcome)

English simply can’t word by word translate to all ways because this compound word is already taken for something different while French has toujours (tous jours / all days)

Other examples are:

de toute espèce (whatever kind)

de toute nature (ditto)

Tout corps plongé dans un liquide… -> Any object, wholly or partially immersed in a stationary fluid, … (Archimedes)

The singular form of "all" is "every" but English sometimes uses a generic all like for example in:

Compare "All men are created equal" with (tous) les hommes naissent et demeurent libres et égaux…

This is indeed common, where tout has the meaning of chaque, n’importe quel(le), albeit maybe more in written French. Some examples:

Tout condamné à mort aura la tête tranchée.

Toute exception devra être approuvée par le directeur.

Je me prépare à toute éventualité.

Il sera traité comme tout autre citoyen.

A tout seigneur, tout honneur (French proverb, it means that any important person is entitled to any honors that are due to them, especially when giving them some sort of priority).