Almost exactly my story. I drink or eat kombucha with almost every meal, or sauerkraut, and always take my magnesium - and a big dose if it's been more than two days since I went.
This is good. I feel like an expert in constipation. Had it for 8 years. Did everything the docs said and nothing helped.
Here is what worked for me; it took about 4 months but the result is perfection on the poop scale.
Eat 60-65% fats, 20% protein, 15% carbs. The carbs should include a lot of leafy greens to provide soluble fiber and lots of the cabbage family, both cooked in CO or boiled. No starches such as potatoes.
Magnesium daily, Probiotic capsules before every meal, plus those mentioned by Damiana.
Never let constipation build up. If you're constipated (no poop) one day, take Milk of Magnesia that night. Every time. It's safe and harmless and works wonderfully well. You will not become reliant on it.
Steak, eggs, potatoes - fruits, nuts, berries and forage. Coconut milk and potent herbs and spices. Tea instead of coffee now and teeny amounts of kelp daily. Let's see how this does! Not really had dairy much, and gut seems better for it.