Filling garage floor control joints
The purpose of backer rod is simply filler so that less caulk is required. This is desirable for (at least) two reasons: Caulk isn't free. Also, it cures because of exposure to the atmosphere; if applied too thick the caulk at the bottom of a joint may not be able to cure. Your joints look shallow enough that backer rod won't be useful.

The self-leveling sealants from Sikaflex are great. However, there's something to beware of: after the material is applied it remains flowable, albeit slowly, for some time. This can result in unpleasant time-delayed surprises for the beginner.

One is related to foam backer rod -- it floats. In case you use any foam fillers, ensure they're stapled, glued, or otherwise well-attached. Otherwise you may find that after some 10-20 minutes the foam floats up to the surface of the sealant. You poke it back down; it slowly surfaces again.. eventually the sealant sets with at least some of the foam visible.

Another surprise is that the sealant will drain, slowly, into large cracks. It looks like you do have a few of these. One way to deal with this is to plan on multiple applications. Apply sealant directly into/onto the crack, just enough to cover it, and wait for that to cure. Some may drain into the crack, but it'll coat both sides of the crack and the gap will be smaller. After one or more repetitions of this the gap will shrink to the point that there's no more appreciable drainage into the crack. Go ahead and fill the entire joint at this point.

After you've been working for 5-10 minutes go back and look at the area where you began. If the self-leveled surface is lower than you like then you can add a little more material. It'll settle and blend in. If you wait too long (the first application has skinned over) then the second application would sit on top of the first rather than blending in.