My experience is from actual play. It is what pointed out to me how OP the spell can be. It gets worse and worse the higher level you go. At low levels it is just a different/worse shield. When used against attacks it is fine. When used against skill rolls, it is interesting. When used to push through spells it is OP.
When used to try push through spells it usually fails at this. If your table has a different experience, and it happens often, that is a statistical anomaly. You either have a lot of enemies with poor saving throws rolling abnormally great on the first roll or a lot of enemies with great saves rolling abnormally poorly on the reroll. People call it disadvantage, but it is not disadvantage as the triggering reaction requires a successful save.
When used to reroll attacks that are not crits it is also usually a waste for nearly the same reason.
The most power SB ever has is when DC is natural 11, in which case it is 25% effective at changing the outcome of a spell, meaning it will work once out of every 4 higher level spells you cast. That is a significant boost, but you don't have enough high level spell slots to make it a huge or OP boost or one that will often matter. Even at 20th level you only have 6 spells of 6th level or higher per day.
The problem is that enemies generally have a very small chance of resisting spells at high level, unless you are using something that is clearly the wrong spell. It takes a 1/5 chance of resisting and makes it a 1/25 chance.
Ok so here is the math on this and why you are wrong mechanically -
A 15th level Wizard has 3 spells of 6th level or higher to cast per day and based on this the enemy already has an 80% chance of failing. Having SB prepared and ready moves it a little bit to a 96% chance. However if the enemy has a 1 in 5 chance of saving against your high level spells, then most days you will not get to cast silvery barbs to "force" a high level spell at all, because the majority of days an enemy will never make a save against your high level spells to start with. If this is the reason you have it most adventuring days it will not be cast at all, it will take up a spot you could have something else prepared for. Considering the high level spells available, this means at 15th level you are preparing SB which will usually go uncast (for this use) when you could be preparing another 6th, 7th or 8th level spell and have more options available.
If you wake up from long rest with Silvery Barbs and you use all 3 of your high level slots on save or suck spells against someone with a 1/5 save, your chance of SB being successful at changing the outcome on one or more save is 40% per day assuming it is a combat heavy day where you burn all your high level slots. So on average it will be 2+ adventuring days before this works for you one time.
Now when BBEG makes that 1/5 save on the crowd pleaser and you have it in your back pocket, then yes it is pretty awesome, but a spell which is only useful for something once out of every 2-3 combat-heavy adventuring days can not be overpowered. That is
"situational".
The mathematical relationship between the triggering save and the reroll ensures that successful uses are limited in a large sample size. If you reverse the situation and say your enemy has an 80% chance of saving (4/5). Then you could be casting it a lot, but it will not be very successful as it only cuts the chance to save from 4/5 to 16/25 (and when you cast it the first is already success so there is a 4/5 chance of saving when you burn the reaction. This means you will have more opportunities and use it more, but it will be unreliable and when it does finally land will be unpredictable. Further the cost is very high in this situation as it will cost 6 levels of spell slots and 5 reactions to reverse a single spell on average.
At high levels it is the opposite of what you are describing. It makes landing a spell on an enemy way too likely. There is no real price for failing your 5th level slot, you just spent a 1st level spell and effectively get another try at a high level spell.
At high levels most relevant enemies have legendary resistance, which makes it useless for this until you run them out.
Further losing a reaction is a huge price to pay at high level. Cast Banishment on a Red Dragon that is out of legendaries and the most common outcome is that he makes his save twice and you are likely down as you can't cast shield, counterspell or absorb elements.
For it to be mathematically likely to change the outcome the enemy has to make a hard save on the first roll. That does not often happen.
There are times when it is effective, but again that is situational.
When it was letting you reroll a save on a hold person etc it was powerful but not insane. When a 1st level spell is basically giving you another chance at Dominate Monster, or Banishment, it is OP.
The problem here is he needs to make the save to start with. Monsters that do that the first time are likely to do it the second as well. The chance of making a hard save is statistically small and the chance of failing an easy one on the reroll is also statistically small, making the combo (sucess-fail) always small.
Using the adult red dragon example above with an 18 DC, the chance of SB successfully forcing banishment is 21%. the chance of forcing Dominate Monster is 25%. That is of course after he used his 3 legendaries, so you had to get him to fail 3 saves that mattered before you even get to the point you can use it for this. How many spells are you going to need to cast to make this happen?
So if you manage to get through his legendaries, and if you manage to still have a powerful save or suck prepared, and if he makes his first save and if he fails his second save, and if this is at a point where the combat is still in question ...... if the stars align and all that happens, then yes SB will save the day and I have seen it do something like that. But that is a very small chance and it is rare that kind of scenario will present itself and the dice will fall to make it reality.