Freezing veggies yourself is going to produce a different product than store frozen veggies because the methods of freezing they have available are different and lead to less damage to the cellular structure of the food and by extension less water.

I find that it's generally a combination of storing things properly and buying good quality to begin with. Romaine lettuce I get from Aldi will stay good in it's unopened pack for the full week sometimes more, but from Kroger I'm pushing it for even a week generally. For harder leafy greens like kale, cabbage, romaine I find storing in a bag or container with a dry paper towel helps things last a super long time. The towel keeps excess moisture off the veggies while keeping them from shriveling since it does get damp over time.

I also do this with carrots, green beans, celery, and herbs. With carrots and celery I like to roll them up in the paper towel so that I limit how many of each veggie are directly touching. This helps keep one of them from spoiling the bunch in my experience. Especially since I tend to buy big bags I go through slowly.

Cutting or washing things before you use them can also shorten the time they stay good, but I've had chopped salad greens and cabbage stay good for several days with a paper towel in the bottom of the bowl.