reckoner
No. Soreness tells you a muscle met something it was not used to. It does not tell you the session was any good, and it does not tell you the sessions that leave you walking normally were wasted.
It is not even a reliable read on the damage
Soreness is taken as a proxy for muscle damage, and damage is taken as a proxy for adaptation, so the belief is two guesses stacked on each other. Reviewing the question, Schoenfeld and Contreras describe the correlation between soreness and the time course and extent of the damage as poor: some muscles are more prone to it than others, and there appears to be a genetic component, so some people are persistently sore while others rarely get sore at all1.
Two people can do the identical session and get opposite readings off the same instrument. That is not a measurement.
The weeks you are sorest are not the weeks you are building
Damas and colleagues followed ten young men through ten weeks of lifting, taking muscle biopsies at the start, at three weeks and at ten. Muscle damage was highest in the first week and fell away after it. In that first week, when damage was at its peak, the rate at which the men were building new muscle protein was not related to the growth they eventually got. At three weeks and at ten, once the damage had settled down, it was2.
So the sorest weeks of a training block are the ones whose response has the least to do with the result. That is the opposite of the folk rule, and it is measured rather than argued.
Why it fades, and why that is fine
Soreness dies away when you train a movement regularly, which is the repeated bout effect, and training a muscle group often would reduce soreness while still delivering results1. Weeks into a program you may not be sore at all. You will still be getting stronger, which you can see, because the weight on the bar is a number and how your legs feel on the stairs is not.
High levels of it are worth avoiding rather than chasing. Schoenfeld and Contreras read severe soreness as a sign the lifter has exceeded what the muscle can efficiently repair, and note that it impedes training and drains the motivation to keep going, which is its own cost1. Their conclusion is that soreness should not be used as a definitive gauge of results1.
What is worth reading instead
Two things you can actually count. What you lifted, meaning the reps you finished and the weight you finished them with. And what it took, meaning how hard the sets were on the day you did them.
Those are available the moment the set ends, they are the same measurement for you as for anybody else, and they are what a decision about next week can be made from. Soreness arrives two days late, varies by person and by muscle, and answers a different question.
What Reckoner does with it
Reckoner asks how you are before the first set, and one of the three answers is that you are rough, which covers sleeping badly, being sore and being drained. Say so and today's loads come down for today only. It never becomes next week's baseline, so a sore Tuesday costs you one session's weights and nothing else.
What decides next week is what you did and what it took: the reps you completed against the target, and the effort you reported at the time. How you felt two days later is not something the engine reads, because it is not something it could act on.