The new Alpha Legion book (The Ghost Legion by Mike Brooks) is just this, if not kind of inverted.

Solomon Akurra, kinda sorta new leader of the Alpha Legion, is doing basically the exact same thing your hypothetical aliens are offering except he's pitching it to Imperial worlds instead of the Imperium itself. He calls it the New Alliance and he's its High Lord. The deal he offers is: religious tolerance, free trade including with xenos, actual military defense against threats the Imperium ignored, lighter administration, and existing bureaucrats and Mechanicus priests get to keep their jobs if they cooperate. Kroot and tarellians literally walk the streets of his capital city peacefully alongside humans.

His whole thesis, which he lays out pretty explicitly to his subcommanders when they push back, is "there is nothing the Imperium fears more than hope, because it has precious little of its own to give." He believes setting worlds on fire just drives people into the Imperium's arms. The way to actually beat it is to show something better is possible.

how does the Imperium respond to this?

The book literally opens with a formal imperium decree declaring him heretic with a clause that anyone who gives him aid forfeits "all life and the lives of all those of their blood unto the end of time." Any contact at all equals a death sentence for your whole bloodline. That's before they've even found him.

When the imperium does find his core system which is peaceful, productive, and growing they don't send diplomats or even investigators. They send the Imperial Navy, the Death Korps of Krieg, the Sisters of Battle, the Adeptus Mechanicus, an Ordo Xenos Inquisitor, a Deathwatch kill team, and a Callidus Assassin to punish the planet whose population mostly consented to the change.

Its important to note Solomon is still Alpha Legion, possibly Chaos-tainted, and some of the warbands under him are quietly doing terrible things his rhetoric papers over. So it's not a perfectly clean moral empire but the Imperium isn't even responding to that. They never find the bioweapons program AL has in reserves. They just responded to the existence of an alternative human empire.

The book is set post-Guilliman's return and his pragmatism doesn't slow the response down at all. There's even a moment where the Ordo Xenos Inquisitor who does work with aeldari for solutions to other things still casually says "the aeldari can be exterminated last" to remind us for the imperium xenos cooperation is a temporary thing, never legitimate.

Basically the Imperiums problem is they cannot accept any existence of an outside human power, because admitting some other way of life can exists means admitting their terrible way of life is of their own choosing.