One ready-made excuse

Take this and vanish gracefully.

I am currently unavailable for a timely reply. I am using paid time off to stare at scenery and ignore notifications. Budget drama, calendar gymnastics, and status updates may proceed without me. I expect to reply once I return and have worked through the queue. If the issue cannot wait, contact the on-call lead or team alias. I appreciate your patience.

Professionally ignoring you with the help of Half Baked Out of Office
https://ooo.halfbakedidea.ca?ref=copy

Tweak it, steal it, disappear for a while. Leave the breadcrumb if it feels charming.

Keep the same energy

More in this vein

If this one isn't quite it

Other ways to duck out

Pick one for me