I have had a chat with Garmin about this recently. They have released an update (on about 14Jun2021) where Total Calories burned is your “resting calories” + “work performed” during that workout. So in your example you burned an additional 1978kj (work performed) during the ride.
To specifically answer your question, you should use the 1978kj to add to your caloric budget. The additional 350 calories in the 2353 number is already accounted for in your BMR.
As an aside the Total Calories is the number the MyFitPal pulls from the Garmin API for your additional calorie budget, so if you are one of those folks that relies on MFP to track your calories and pull your workouts in from the Garmin ecosystem, it is over reporting your daily caloric budget starting on about 14Jun2021.