The multiclass rules exclude Warlock levels from the counting toward multiclass spell slot progression. To me, that means that Warlock "spell slots" aren't spell slots the way that other casters can conceive of them, and really ought to have been called something else to avoid the confusion. By logical extension I'd think that the intent is therefore that Warlock spell slots are incompatible with any non-Warlock feature mentioning spell slots.
Your DM could always rule otherwise, but I would not allow them to be "bottled up" into Artificer elixirs. The short rest recorvery exploit is clearly beyond the intent of either class feature, as its explicitly trying to contort the rules into giving you more spell slots than you should have. The only way to make bottling Warlock spells fair is for (1) the "bottled" spells to expire when you short rest and have to be remade, or (2) lock the Warlock spell slots so they cannot be recovered until the elixir is used.