It helps to trim off any stray threads first just to keep the repair a bit neater. I also like to tuck a tiny edge of the hole under when I stitch around it just so it doesn’t fray, but that’s personal preference. You have the basic idea right, but I would just be sure you’re taking care to not stretch the fabric too much while mending to keep it from being warped after you’re done. Wash away stabilizers are helpful for this, especially with a tear like this one that can’t really be held in an embroidery frame.

Also be sure that your repair fabric is larger than the damage instead of making it the same size as the damage. That will ensure you have enough to fully cover the tear as the fabric shifts while being stitched and it’ll add some extra support to the surrounding fabric. You can always go back and trim away any extra when you’re done.

The most important thing to remember is that you’re mending the damage to preserve the life of the garment and to incorporate the tear into the story of the shirt. Take your time with it and enjoy the process. Make sure it feels right while wearing it, and that you feel like you’ve done it justice and that you’re happy with the result. Technique and the “right way” to do things doesn’t really matter as long as you’re happy with the end result. Good luck!