Awaiting editorial office processing for more than 22 days, Is it appropriate to contact?
Yes, you should. 22 days before the paper is passed on to an editor is out of the ordinary. It's true that it's summer and people might be on holiday, but this is the publisher we're talking about - even if some of them are on holiday, they should have people to cover. Journals don't close shop when the staff are on holiday.

I would contact the publisher. If you know the desk editor's email address that would be the best person to write to; if not, you can use Taylor &amp; Francis's author services contact form.