Is a dry bag necessary during the summer season for the Narrows (bottom up)

Not really. Depends on how clumsy you are hiking.

What do you need to keep dry for a day hike? Put a pair of socks in a ziplock bag to change into about 5mins out of the water on the way back down. If you're worried. Almost all the water will be between ankle to knee deep. And no neck deep holes. You may fall but you basically have to roll around in the river to get your back wet.

To put it in perspective I went up with about $7000 in camera gear on my back, no wet bag, multiple times. And had plenty of slips and falls going up.

Make sure you have a hiking staff, and if you fall do it on your hands and knees like normal.

Probably. Especially this year. I went last year and there was a part close to be beginning where you had to get waist deep in water. Unless you don't plan on carrying anything that can't get wet or only want to to half a mile before you turn back, you'll need something to keep those dry. (But you might also trip and fall into the water since the bottom is uneven).

I got a nyloflume pack liner and put all the things I need to keep dry in there in my trail running pack. My cell phone went in a waterproof phone container so I could still take pictures.

We put phones in zip lock baggies and stored them in the top pocket of a backpack. We didn't hike through the end, but we did like 10km (hello from Canada) and our devices survived.

Yes

I'd high suggest bringing a bag if you plan to hike more than a mile past the paved path in. At times the rocks can be slippery and having a trekking stick or your hands free to catch your fall will be helpful. Also, be careful of toxic cyanobacteria in the Virgin River, so bring your own water.

Make sure you bring a plastic bag to protect your electronics. Water levels are much higher than prior years, so its best to take some extra precautions.