Best way to pack digital camera?

What kind of carryon bag are you using? If it's hard-sided, I would put the camera, in its case, in that, and put that in the overhead bin.
I don't think you have to remove the batteries, as long as the camera is turned off. Only spare batteries and power banks have to be stowed under the seat, from what I can tell.

I have been travelling with an A7 IV and 3 zooms (GM's, 12-200 millimeters range) for several years in a $25 Amazon messenger bag. I store the camera body with the medium zoom on and the two other lenses vertically. I stuff the batteries, a couple of filters, essential papers, a Surface Go, and my on-plane medication into the same bag. It slides under a seat in all Boeing and Airbus aircraft in standard economy. I also don't check in anything and use a 4-wheel roller carry-on for all my other stuff, including chargers, cables, power supplies, and a few other electrical and electronic items. One thing I don't do is put the camera bag in the overhead bins; other than that, I don't take any particular precautions. Works for me, and there has been no damage in the 5 years I have been flying to/from and in Western Europe and to India and back. I have never rented a tripod in Europe; in India, yes, but that was for a documentary video (made with the same gear). Hope this helps.

Many thanks for the quick responses! Giving me things to think about.

I'd caution against packing the camera with lens attached in anything other than a padded camera case.

We put our mirrorless Olympus in a backpack 'under the seat in front of us', and one leg stretch later, the lens' rear mounting ring was completely broken and useless.

Luckily we found the exact same lens at a branch of Best Buy in Mountain View CA; and luckily, our travel insurance reimbursed us for the full cost.

Since then we've packed the camera and the lenses separately, and so far, so good.

My kit is a German rangefinder body with 4 prime (aka single-focal:not-zoom) lenses in a Domke ballistic nylon J5B "belt-and-shoulder bag" (when weight-restricted I use an ultralight ripstop version of it which was a ltd edition now discontinued). En-route it sits in my RS carryon backpack nestled between packing cubes of clothing, stowed in the overhead bin...has not sustained any damage in decades of travel...and it's fully-insured. The one time I nearly had it stolen was at Rome FCO when a lovely young lass attempted to abscond with both my bags as they emerged from the security x-ray.

As for a tripod, whilst I own a svelte 1kg Gitzo carbon-fibre which extends to my eyelevel, I ceased traveling with it in the immediate aftermath of 9/11 and found, despite my camera lacking IS, I did not miss the pod apart from long exposure shots, and even those I find I can usually manage to find some novel means of support. Today digital ISO 6400 nets a far cleaner image than ASA 400 slide film did in times past, and even with my longest and slowest lens, a 90mm f/2.8, I find I can get a sharp shot at 1/60. Your Oly has IS so you ought be able to go 2-3 stops slower. So I'd not think twice about leaving the tripod at home.

Thanks for your replies! I’m starting to get a handle on this packing situation. Will definitely leave the tripod at home.