Why did my ginger garlic paste have a bitter aftertaste?

I see three possibilities based on what you've said:

• the germ of the garlic. The germ, or new sprout of the garlic, should be removed before cooking. If your garlic had started to sprout and especially if you left in the germ, this is a possible cause of the bitterness.
• acid. Cooking garlic in an acid environment can cause chemical changes in the garlic, such as turning blue-green or bitter -- as in your picture. Ginger and onions might even be enough to trigger this, or other components of the dish.
• over-cooking the garlic. Though you said you were careful with heat, it's easy to burn garlic just enough to make it bitter.

The green color of the paste is telltale for a lot of properly sprouted garlic... as hoc_age already said, the sprouts turn bitter when cooked, so break up your garlic and remove anything green inside before making the paste. Also, blenders tend to oxidize oils, if the result is still not satisfactory, try using a mortar and pestle instead - garlic and ginger are easily broken down in a mortar if coarse salt is added and used as an abrasive... just remember to put less salt in the dish!

Cooking ginger/garlic paste too long at high heat (that didn't burn because it was premixed into a couple cups of yoghurt/spices/meat), seems to have caused the bitter taste in the portions of the meal that were towards the bottom of the pot.

• I have an Indian recipe for Hyderabadi Chicken Biryani that calls for 4 Tablespoons of Ginger Garlic Paste mixed into two cups of yogurt, along with the meat and spices and top layer of par-cooked rice. Normally the mixture is cooked on the stove in a lidded pot for 5 minutes on High, 15 minutes on Medium and 10 on low. The juices from the meat mix with the yoghurt mixture and everything works out well.
• I've made this dish several times with success, so thought to change it up, and not having goat on hand I used beef sirloin instead of chicken. So I thought I would need to switch to a pressure cooker pot to make sure the beef is tender, instead of the regular pot, and cooked it for 10-15 minutes on High and remainder on Medium.
• The bottom layer did not discolor as if it was burned, however I tasted bitter portions throughout the dish, and moreso as I mixed the cooked dish completely. Adding lemon helped, but now I have a pot full of tender beef, occasional bites that are good, and the rest that is sooo bitter! Next time I will use the regular pot approach, and just cook it longer on low to make sure the beef is tender and the Ginger Garlic paste does not overcook to become bitter.

When you add the garlic paste, don't stir it too much, and don't put garlic paste in oil when there is nothing else in it.

When the raw smell of garlic goes away, that means it's cooked through, it won't have the bitter taste.

I have struggled with this too and after very carefully making and remaking a recipe (4 times in one day), I found the problem was with the ginger. The longer the recipe cooked, the more bitter it would become until it was inedible. I bought new ginger thinking it could just be old but the same thing happened so I take the fresh ginger out completely and just add some powdered ginger later on in the recipe. Haven't had the problem since. I wish I could use fresh but it just won't cooperate. Maybe I am cooking it too hot

Overcooking Ginger is the cause

Ginger if overcooked in sauce masala, tea etc gets bitter and loses its flavour.

Garlic can be burnt a little and it gives a good flavour (umami taste i think)