I think it’s a bit different than this, spells may prioritize Warlock spell slots if they are only available from the Warlock class, but in my experience spells that are available from multiple sources (e.g Counterspell and Armor of Agathys) will be completely uncastable with Warlock slots until you have used all non-Warlock slots of sufficient level even if you have only learned those spells through the Warlock class.
In my specific example, playing a Warlock 5/Wizard 7 multi class, learning Counterspell at Warlock level 5 and not at any point while leveling Wizard, I am not able to use a Warlock slot when casting Counterspell as a reaction even though the UI displays the option to respond using a Warlock spell slot. I am also not able to cast Armor of Agathys using a Warlock spell slot as long as I have any non-Warlock spell slots available. Even clicking the Warlock slots in the UI, then clicking AoA, I am then presented with the option to choose which level I’d like to cast AoA at showing only my non-Warlock slots.
This is as GOO Warlock, as some things I’ve seen suggest this is somehow less of an issue for Fiend?