"on the Adjustments to Income"

A Roth contribution doesn't adjust income. That's also why recharacterizing it to Trad IRA also means nondeductible. It's post-tax dollars. There is no tax benefit for putting away those funds. It will be Basis.

"If the Roth IRA recharacterization to Traditional IRA was eventually converted back to Roth IRA,"

Fixed it for you. It is converted to Roth, the same as any other funds would be converted. There is nothing special about it, because it came from Trad IRA. Each step along the process stands alone, and not in reference to the earlier.

"does the traditional IRA contribution that was converted"

Take them one at a time.

The amount put to Roth is moot, since it was recharacterized = Oops, I made a mistake.

The amount converted from Trad IRA is going to trigger a 1099-R, because a conversion is a distribution, even if a direct transfer to the other account or trustee.

"need to be entered as a nondeductible contribution on Form 8606?"

Yes, it was a nondeductible Trad IRA contribution. That's the place were it is contribution. It's Basis = post-tax. That's why I keep bringing "pro rata taxable" into the discussion.