RAW: there is a spell called "Trap the Soul" listed on page 211 of the PHB. It is a Wizard spell. Oddly enough, there isn't a spell description to accompany this spell (...and it was errata'd out in later printings. I have a first printing PHB).

RAI: it appears that there was at one time the intention to have a soul trapping spell, but it never made it to print. The function was folded into the "Imprisonment" spell.

See page 252 of the PHB for details of the Imprisonment spell. The Minimus Containment feature, one of five options, seems to meet your criterion of

I wanted the classic "soul trapped in an object" feel.

The target shrinks to about one inch in height and is described as being stuck inside of a gem.

As to "not being able to escape" that will always depend on if this entity / person / demon has any friends who could free said entity. If you keep the gem / prison on your person, then you'd have to be overcome before this entity could be freed.

You'd want the same hope of some chance of being freed if it were cast upon you, I suspect.

In Magic and in D&D, as in war, nothing is final.

Xanathar's Guide to Everything may have filled this gap

In @Vylix's answer, the Soul Cage spell from XGtE fulfills some of the requirements.

The closest thing I can think of in 5e...

(Tomb of Annihilation spoilers ahead; not just little stuff, but the major unknown-at-first plot-point of the whole shebang.)

The dangerous artifact in Tomb of Annihilation hidden beneath the eponymous tomb is an Acererak-created one-off called The Soulmonger. The Soulmonger has two linked abilities.

(a) To vacuum up any souls that leave their body and intercept them before heading to their planar/religious/whatever-happens-to-souls-in-your-cosmology destination, making resurrection magic null and void (since the souls aren't available to stuff back into the/a body).

(b) To slowly draw souls that have previously been re-stuffed away from their body. This "death curse" manifests as any creature who's ever been the recipient of resurrection magic losing 1 hp off their max per day until they hit 0, at which point their soul is hoovered by the Soulmonger. This is the bit I think has some relevance for you.

We can see here that losing your soul does have mechanical relevance: you die without a soul. Period. Full stop. Even wishes are going to have a hard time countering this.

Though see "Nanny Pu'pu" in Tomb of Annihilation for a slight workaround.

So what should you do with this information? I'd suggest that immediate death is a silly outcome: it stinks for the player, and if the devil could do that as part of the bargain,why would anyone ever be alive "waiting" for their deal to come due? But the examples do suggest a mechanical, incremental, detrimental effect^* that the devil could be able to exert on the character.^** Whether this happens every in-game week, or every time the character does something the devil doesn't like, that's up to you. (And the player, if you want to share this bit of worldbuilding.)

^{* it's the}

HP max loss, just to spell it out clearly

^{** - It's come to my attention that there are two different ways of thinking about what's going on here; they're both interesting (IMO) and don't seem to change much of the end-effect, but I'll spell them out just to be clear:}

^{1) The deal made with the devil gives the devil the power/ability to siphon away bits of it occasionally, until it's all gone and the character's dead;}

^{2) The deal immediately transfers the soul to the devil's possession but they use some magic to keep you going in some state of "life, but with conditions" (compare with magic jar or clone or the like).}

^{Either way, the devil's got their hooks in the character.}