So 3 reactions and 3 first level slots was half as good as 6 actions and 3 4th and 3 5th level slots in effect.
To start with I did not consider magic resistance, which makes it a lot worse. But even going with a subpar DM that does not realize this )me) - It is still not as good as 3 uses of Absorb elements against fireball which would have saved on average 42hps damage (or 84 with failed saves) .... enough of a difference to kill a 13th level wizard outright.
The entire strategy is a bad one and preparing those spells in place of things like absorb elements and false life is not nearly as effective against this enemy or for that matter most legendary enemies.
As for Bel, say we use Psychic Lance (int save). 21 DC (+2 DC item!), needs a 14+ (+7 int save). Advantage makes it 60% save chance, but reroll from barbs isn't a save.
So you need a +3 to get a 21 DC at 13th level. You are also adding a magic item that is not present in the very campaign where Bel's stats are published and more powerful than any item in that adventure save one. For reference, I finished that campaign with boots of elven kind, an immovable Rod an no other magic items..
Let's go with this example though. Using a +3 item (21 DC, +13 Spell attack)) - He needs a 14, his chance of saving with magic resistance is ~58%.
We will assume Bel is going to fireball you every turn and you have a +4 dex save for an average of 22dpr if he can target you.
Psychic Lance With Barbs: If you used all three of your 4th-level slots at the end of three turns you would have used on average 3 first level slots, 1 silvery Barbs (1.2 mean) and stripped 2 Legendary Resistances (mean 1.2 remaining), one of them with silvery barbs (0.8). On average Bell would have taken 37 damage total over those 3 turns. This would have cost you 3-4th level slots, 1-1st level slot, 3 actions and a reaction. You would have caught the full brunt of 3 fireballs.
Let's compare this to other first level spells you could have prepared instead of barbs:
Psychic Lance with Expeditious Retreat
You prepared Psychic Lance but expeditious retreat instead of Barbs. You use a Chill Touch cantrip the first turn when you cast ER: Bel would lose 1 legendary (mean 2.1 remaining) and on average would have taken 25 Psychic Damage plus 13 Necrotic Damage. You can exploit the full range of Psychic Lance and move out of range every turn after casting expeditious retreat and chill touch on the first turn. He can't fireball you at all.
Magic Missile with Absorb Elements: You prepare Magic Missile and Absorb Elements instead of PL and Barbs. Magic Missile is a GOOD spell, not OP but good. If you had used Magic missile cast at 4th level every turn Bel would have taken 63 Damage on average. You can use your reaction to reduce fireball damage. Note if you have a move higher than 30, you can actually move out of range one of these three turns.
Expeditious Retreat and Cantrips:. Going only with cantrips casting expeditious retreat and using absorb elements. Casting expeditious retreat on the first turn and stayong out of range. You deal on average 41 damage with just cantrips. He can't fireball you at all.'
Absorb Elements and Blink: You prepare Blink and Absorb Elements instead of Psychic Lance and Barbs. You use Chill Touch to attack. On average you do 27 damage and avoid 1.5 fireballs completely, while halving the other 1.5.
Absorb Elements and Summon Fey: You prepare Summon Fey (upcast 4-th level) and Absorb Elements instead of Psychic Lance and barbs. You use Chill Touch to attack after the first turn. The Mirthful Fey causes a charm save and attacks every turn. For this we will assume Bel attacks you with fireball. If he attacks the Fey it is even better. The Fey does 21 DPR, Chill touch does 13.5.
Haste and upcast Magic Missile: You prepare Haste and Magic Missile instead of Psychic Lance and barbs. You cast Haste the first turn and use the haste action to dash out of range every turn while unleashing a 4th-level magic missile with your action.
Results:
Psychich Lance with Barbs:
You take 66hp damage. With a 10 constitution you are down. With a 12 constitution you have 1 hp left.
Bel takes 37 hps, loses 2 LRs
Cost 3-4th, 1-1st, 3 actions, 1 reaction
Psychic Lance with expeditios retreat and chill touch:
You take 0 damage.
Bel takes 38 damage, loses a LR
Cost: 2-4th, 1 1st, 3 actions, 2 bonus actions
Upcast Magic Missile with Absorb Elements:
You take 33 damage
Bel takes 63 damage
Cost: 3-4th, 3-1st, 3 actions, 3 reactions
Expeditious Retreat and Chill Touch
You take 0 damage
Bell takes 41 damage
Cost: 1-1st, 3 actions, 2 bonus actions
Absorb Elements and Blink
You take 17 damage
Bell takes 27 damage
Cost: 1-3rd, 1.5-1st, 3 actions, 1.5 reactions
Absorb Elements and upcast Summon Fey:
You take 33 damage
Bell takes 90 damage and loses 1 LR
Cost: 1-4th, 3-1st, 3 actions, 3 reactions
Haste and Magic Missile:
You take 0 damage
Bell takes 42 damage
Cost: 2-4th, 1-3rd, 3 actions
So yeah, I don't see this awesome advantage you are supposedly getting by casting Barbs. I just gave you 7 examples, one using Cantrips only to attack, all of them are an objectively better outcome at the end of 3 rounds.
Even if you assume the area is confined, such that you can't get out of range, almost any non-fire and non-poison combat spell you take with absorb elements is going to work better than the same spell paired with SB.