A big established rose recently transplanted in Zone 10? I’d fertilize right now!

On a transplanted rose, I wait until I see some new growth which is where you seem to be now.

All we've done is amend the soil around the hole with some good potting soil

Amending of planting holes for long term plants with root systems of some size is obsolete practice that was starting to be seen as counterproductive in the late 1960s.

So you should dig the rose back up, remove the potting soil from the hole and refill the hole with the same dirt that came out of the hole when you dug it. So that the dirt in the hole is the same as the dirt around the hole.

After re-planting the rose in the original dirt, put the potting soil over the top - as mulch.

If instead of the backfill being pretty much all potting soil as it stands now, you have planted in a blend of the two then dig that blend out, get some dirt like what was in the hole before you amended from elsewhere on the site and re-plant in that.

There is no reason to withhold fertilizer from recently planted stock - if, as always, a need for fertilization has been determined. If this rose has a nice deep green color, maybe it doesn't need any.

If you are seeing new growth since you transplanted it go ahead and fertilize.

Embrothrium:

If the rose was happy in the good potting soil in the pot, why would the rose not be content in the hole with good potting soil as backfill, as long as one ensured adequate nutrition without overwatering? I’m asking about the rationale.

The rose is going in the hole with the rootball comprised of good potting soil.