While a guy like White might be cheaper than someone like Tannehill, I would rather go with a fully proven vet. I will admit, I don't know a lot about White, but his stats are very unimpressive, so I don't see him as being much of an upgrade over what we already have.
If the Packers do try to sign a vet QB to backup Love, they should do it sooner, rather than later. Doing so will give that QB more time to get up to speed and once the season starts, injuries to other starting QB's will dilute the available FA QB's.
A season can be changed in the first 4 or 5 snaps, ask the Jets.
My prediction, Gute rolls with Pratt and puts Clifford on the PS. Probably the rationale, even if Love goes down, a guy like Tannehill won't take the Packers to the SB. Bank the savings, develop Pratt and possibly go all in for 2025.