One ready-made excuse

Take this and vanish gracefully.

I appreciate the email and regrettably will not be reading it promptly. I am away collecting sunburn, questionable snacks, and plausible deniability. Cross-functional anxiety should be routed through someone with more availability. A reply will follow when normal operations resume. For urgent matters, please use the existing approval path instead of guessing. I appreciate your understanding and 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