Here's what Assurance has to say:
Even in the worst circumstances, you can perform basic tasks. Choose a skill you’re trained in. You can forgo rolling a skill check for that skill to instead receive a result of 10 + your proficiency bonus (do not apply any other bonuses, penalties, or modifiers).
If Assurance literally forgoes a roll, does this mean effects that are based on a roll result do not work with Assurance?
At first glance, I assumed Assurance simply replaces your roll result with 10 + your proficiency bonus. You don't roll but have a roll result nonetheless to determine success. For example, I was always under the impression that 'rolling a success' was equivalent to 'get a success' or 'succeeding at a check.' Now I'm wondering if there's actually a difference and the omission of the word 'roll' could be significant in some effects.
Most effects mention a roll or rolling like Assured Identification:
You rarely misidentify an item. When using Arcana, Nature, Occultism, or Religion checks to Identify Magic, if you roll a critical failure, you get a failure instead. If you would misidentify a cursed item because you roll a success but not a critical success, you simply can't identify it instead.
Some do not mention rolls at all like Dubious Knowledge:
You're a treasure trove of information, but not all of it comes from reputable sources. When you fail (but don't critically fail) a Recall Knowledge check using any skill, you learn a bit of true knowledge and a bit of erroneous knowledge, but you don't have any way to differentiate which is which.