Mom to an 8 y/o child who has a stutter advice

Mom to an 8 y/o child who has a stutter advice My 8 year old son has a stutter. It started when he was 4-5 and seems to be worse when he is overtired or anxious. Sometimes he will go months without it at all and then months where it is hard for him to get a complete sentence out. We have talked to him about it and asks if it bothers him or other kids comment on it. He said they occasionally do, but it doesn’t bother him personally, aside from hoping other people are not bothered by it. We assure him that it does not annoy/bother/upset us in the slightest & wouldn’t change a thing about it him. It has been pretty constant since school started 6 weeks ago. I don’t know the vocab yet, but he seems to stutter more on words that start with a vowel and he will repeat the same letter/sound… for example “i-i-i-i-i want to e-e-e-e-eat dinner soon”. I’ve asked how it feels and he says it is just automatic and he cannot help it. He also shows signs of facial straining/not breathing during those really hard times. We try to leave an open line of communication for him to talk about how things make him feel & he is great at expressing himself to us. We recently had his yearly checkup and his pediatrician recommended we see a speech therapist. I have seen mixed reviews from adults who have a stutter about the impact of speech therapy on their stutter, with some saying it made it worse to call so much attention to it. Does anyone have any advice? Should we try it and see how it goes or just let him manage naturally? Any thoughts would be beneficial. Neither me or my husband stutter or have any family that do, but we do have a close friend who is a lawyer that had had a stammer his entire life. Thanks in advance!!!