Assuming I’m the DM, I do. But I determine it in the moment based on the action declared. Rather than an objective DC20 History to learn that it’s the seal of king whatshisname and he worked with demons, floating there, independent of any action declarations, I will evaluate each goal and approach independently for chance of success, chance of failure, consequences for failure, and for difficulty if it has all of the above. In the previous post, the three different example actions I provided might all have different difficulties and yield different information.
The character who said they would think back to their time studying with the Dwarven smiths of madeupname (approach) to try and remember if they’ve seen that symbol before (goal) might, for example, succeed automatically if the seal was crafted by that group. You studied with them, you’ve definitely seen it, no chance of that approach failing at that goal.
The player who said they thought back to their study of Dwarven history (approach) to try and remember any details about king whatshisname (goal) might have read that, or might not have, and I could allow progresss with a setback on a failure, so I might call for an Intelligence check - DC 10 if this king guy is well recorded, DC 15 if he’s a bit obscure, DC 20 if information about him is obscured or hidden. I might even scaffold different bits of that information to the different DCs, with failure perhaps meaning that the character has read the name before, but doesn’t recall any pertinent details.
The player who said they would study the seal (approach) to look for any symbols influenced by Infernal (goal) might fail if none of the symbols on the seal are influenced by infernal, as there would be no chance of the approach succeeding in accomplishing the goal. It is indeed the seal of king whatshisname.
These are all examples I’m pulling out of thin air, of course. To give more confident rulings I would need more context. But the point is, there’s no objective check that exists independently of the characters’ actions. What you might learn and if you need to make a check to learn it depends entirely on the task you describe; what you’re trying to achieve and how.