51 cards where the card types include “rat” and (the card is available on Paper) and the mana value is even and the color identity ≤ BRU

Ashcoat of the Shadow Swarm (Jumpstart 2022 #19)
Azure Beastbinder (Bloomburrow #41)
Blightbelly Rat (Phyrexia: All Will Be One #85)
Burglar Rat (Foundations #170)
Dirty Rat (Unsanctioned #34)
Dirty Wererat (Odyssey #130)
Disease Carriers (Urza's Destiny #57)
Earsplitting Rats (Judgment #65)
Gobhobbler Rats (Ravnica Remastered #185)
Graf Rats (Eldritch Moon #91)
Gutter Skulk (Gatecrash #67)
Hellhole Rats (Dissension #113)
Ink-Eyes, Servant of Oni (Planechase Anthology #33)
Innocuous Rat (Duskmourn: House of Horror #103)
Insatiable Frugivore (Bloomburrow Commander #18)
Kuro's Taken (Saviors of Kamigawa #79)
Lightshell Duo (Foundations #157)
Locust Miser (Saviors of Kamigawa #80)
Mind Drill Assailant (Bloomburrow #225)
Mukotai Ambusher (Kamigawa: Neon Dynasty #112)
Nashi, Searcher in the Dark (Duskmourn: House of Horror #223)
Nezumi Bone-Reader (Champions of Kamigawa #127)
Nezumi Cutthroat (Masters 25 #99)
Nezumi Graverobber // Nighteyes the Desecrator (Commander Anthology Volume II #71)
Nezumi Informant (March of the Machine #120)
Nezumi Prowler (Kamigawa: Neon Dynasty #116)
Nezumi Shortfang // Stabwhisker the Odious (Champions of Kamigawa #131)
Ossuary Rats (Jumpstart 2022 #24)
Pack Rat (Return to Ravnica #73)
Persistent Marshstalker (Bloomburrow #104)
Rabid Rats (Stronghold #67)
Rancid Rats (Shadows over Innistrad #130)
Rat Colony (Dominaria #101)
Rats of Rath (Tempest #150)
Ravenous Rats (Duel Decks Anthology: Garruk vs. Liliana #37)
Refurbished Familiar (Modern Horizons 3 #105)
Rotting Rats (Planechase #39)
Ruin Rat (Hour of Devastation #75)
Shoreline Looter (Bloomburrow #70)
Silver-Fur Master (Kamigawa: Neon Dynasty #236)
Sinuous Vermin (Conspiracy: Take the Crown #46)
Skullsnatcher (Planechase Anthology #36)
Swarm of Rats (Ninth Edition #166)
Tangled Colony (Wilds of Eldraine #113)
Thornplate Intimidator (Bloomburrow #117)
Thought Shucker (Bloomburrow #77)
Thriving Rats (Kaladesh #102)
Vren, the Relentless (Bloomburrow #239)
Wave of Rats (New Capenna Commander #41)
Wick's Patrol (Bloomburrow #121)
Wick, the Whorled Mind (Bloomburrow #120)

This search is finished. Now the real work can begin.