One ready-made excuse

Take this and vanish gracefully.

I appreciate the email and regrettably will not be reading it promptly. I am using paid time off to stare at scenery and ignore notifications. Any request involving alignment, sign-off, or strategic visibility can hold. I expect to reply once I return and have worked through the queue. For urgent matters, please use the existing approval path instead of guessing. Thank you for your consideration.

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