Anyone know how this is supposed to work in 5e?
Basically, the 5e rule falls back to the general rules for spellcasting, because it is not ruled on specifically to be otherwise.
What this means is that if you know the spell, you know the spell. Spells you know can be cast with any spell slot equal to or higher than the base level of the spell, and some spells grow stronger or gain extra benefits when cast using a higher slot. That's it.
So, yes - We know these spells, and by definition we should be able to use any appropriate spell slot to cast or up-cast them.
This is true of any spell that you know, from any source, unless it is specifically ruled otherwise (There are some cases where the feature that grants the spell specifically says it can only be cast at its base level, for example. If it doesn't say that, then it's not the case).
Even in the case of feats and features which grant you spell, and use the language "You know the [Spell] spell, and can cast it once at its base level without expending a spell slot. You must complete a long rest before you can cast the spell using this feature again." They use that language very specifically - it's not lazy or pointlessly long-winded, but rather it is specifically noting that you know the spell. You can cast it for free using the feature, sure.... but you know the spell, and thereby you can also use your slots to cast it if you want to.