If this tree were mine, I'd let it have the rest of the year to recover. If still green late winter 2024, repot, and again left a season to recover from the repotting.
Spruces tend to be a "one insult per year" sort of tree. If you have experience you can certainly work them more than once a year, but especially if you are new to spruces, once a year is a good "beginner guide".
Timing - in the Midwest, Illinois, Wisconsin, Michigan - the climates I know well, the best time of year to work on spruce is the middle to end of August. I save all my pruning and wiring for the weeks August 15 to Aug 30. I'm close enough to Lake Michigan I can repot in this time window but if you are outside the "Lake Effect" zone, repotting should be done in late winter or early spring. Everything else should be done in middle to end of August. By middle of August the new buds that will grow the next year will have formed, so the timing is good for pruning back to compact the tree. Pruning in spring you can not see where the back buds are, or will form.
General suggestions for spruces work for all species and cultivars of spruce. Or at least almost all. There are a few exceptions.
On to Dwarf Alberta Spruce, DAS, in particular. DAS is a cultivar, propagated from a mutant seedling of the white spruce, Picea glauca. All DAS are considered Picea glauca, but they have some weird quirks. DAS branches keep a perpetually flexible, a juvenile habit that means no mater how many years the branches have been wired, after removing the wire the branches will rise back up, reaching for the sky.
You can just keep wiring and rewiring the tree. Older thicker branches will "calm down" and can be held down with perhaps just a guide wire after a few years of aggressive wiring, but DAS will always have to have wire on it if the branches are not rising up to the sky.
Or you can design the tree taking advantage or design to the natural tendency of DAS to reach for the sky, keeping the rising habit. Work on creating dense pads above the branches as the branches and trunks reach up.
Generally I recommend against buying DAS if you don't already have one.
Picea glauca, the wild form of white spruce is excellent for bonsai, and the Black Hills Spruce, a geographic race of the species is even better for bonsai. Look for Picea glauca densata, the Black Hills Spruce, that is the best of the North American spruces to grow in the Midwest. It tolerates low elevations, high night time heat in summer (well higher than englemann and other mountain spruces) and tolerates low humidity. Species of spruce do not tolerate high night time heat very well, this is why spruce are not found in southern Louisiana, Alabama, Mississippi, much of Florida and other low elevation, coastal areas.
But for your next spruce, choose Black Hills Spruce. The DAS is fine to learn on as a practice piece, but Black Hills Spruce is just as inexpensive and is MUCH, MUCH better for bonsai. Colorado blue spruce is good for bonsai too, but best for LARGER SCALE bonsai, Blue Spruce are best for trees in the 3 to 5 foot range. There are no absolute rules, try what you want at the size range you want, but these are my suggestions from experience.
Black Hills Spruce works in any size, and wonderful old collected specimens can be had (at a price) from Golden Arrow Bonsai and other collectors.
Most experience growers just don't won't bother with DAS due to its perpetual juvenile habit of branches always springing up and reaching for the sky,.