I'd take some time to fix the patches and seams. Invest in a wide taping knife, and use it to knock off the high spots on the patches and seams now. Then skim with the same broad knive and some lightweight taping/patching compound, applied thin and feathered well. If there are marks when it's dry, you can knock them down with the knife again. Hard edges feather with a damp sponge.
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I did some plumbing work in a garage wall that's shared with the pantry. Me working on the pantry side finishing the plumbing and drywall work. K on the other side decided that the garage wall needed paint before the patching was finished out and texture applied. (!!!) It was like that for about a year before I decided to grind off the unfinished patches and start over. The paint meant that the patching couldn't be finished with a sponge anymore. So cabinets came off the wall, whole thing re-patched and finished, textured, then prime and paint. Looks great, but would have been a LOT easier to do it right the first time.
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Texturing hides a lot of sins, but none bigger than the texturing is thick, so you need to have a pretty good wall before you spray. It absorbs/dries at different rates on drywall vs patched areas, so a coat of PVA first is always a good idea. The bag of wall texture itself is really cheap, and you can rent a gun or buy a cheap one. Garage wall is a good place to practice and learn. Plastic sheet where you don't want it to go, cleans up with water.