You are doing just fine, MK. Keep paying close attention to your child. If you hadn't up to this point, you wouldn't have ended up with a thorough evaluation. It is ABSOLUTELY NORMAL for you to question what is happening with your child.
Early intervention is the key to dealing with learning/developmental differences or delays. The speech therapy he is having is key. But even more important is the work you do with him at home. You should be watching his speech therapy carefully, taking notes, and doing the home program every single day, twice a day. Morning and night. Your little guy may balk, but it still gets done.
Let me talk about that a little bit to you. Speech therapy is hard work! My son decided that he was tired of it, no matter that we couldn't understand most of what he said. At 3 years old, he had a meltdown during therapy one day, and wouldn't work with her. As you know, speech therapy is expensive, and I could not afford for him to be doing this. I took him home, put him in his room and told him point blank that he was being punished for being mean to "Miss Betty". I brought him a sandwich and supervised occasional trips to the potty, but he had to stay in his room all day. When he realized I meant business, and that he was NOT getting to come out of his room, he volunteered to me that he would be nice to her from then on and would work with her. I immediately sat down and did a full lesson with him, and then let him come out of his room. He never pulled that stunt again.
Sometimes you have to do "investigative work". I knew something was "off" that they weren't finding. I asked for an OT evaluation, and nothing came out of the eval. But the speech therapist listened to me and went to the OT on my behalf and told her that I was really good at discerning issues with my son, and would she just work with him some? She did, and by the end of the first session, she told me that he did indeed have sensory issues that needed to be addressed that had not shown up in the eval. It was astonishing to me to watch all the things he could not do in that session. I wondered why her eval didn't address these things? (I think she modified her evaluations after that...) He did 6 months of OT with her, and it made a huge difference.
So the thing I'm trying to say is that sometimes you can't take a single eval's results "to the bank", so to speak. If I had just accepted the OT's original eval results, he would not have gotten the help that he needed. You already know he has some sensory issues. Remember, when there are sensory problems, children seek it out in all kinds of ways. You give them a "sensory diet" that helps retrain their nervous system. The earlier you work on it, the better the results will be. I do hope that you will get him some occupational therapy, along the lines of what I've been talking about. It makes so much difference for a child who has some sensory issues.
I do think that you've gotten some really good results on the speech and language front. You have benchmarks to meet and between you and the speech therapist, you can meet them. You need to put a lot of work into this. The language work is so important. She can give you "carryover activities" for language while they are developing his speech skills to help you at home. He loves order - work with that! As he gets older, work with him on organizing his brain - show him pictures that tell a story, and have him help you put them in order. Having cards that you lay face down in rows, where you find the matching card will help with memorization. These are in education stores, and the speech therapist can help you find similar aides.
Even if your child does not have ASD, he has delays that need to be addressed. Look at this as an adventure with your son to get him school-ready. Once he gets to grade school, you don't want to have to start this adventure then - school moves fast and you don't want him to be behind.
Ask your speech therapist for names of books to read, especially about your son's penchant for repetition. One of the posters gave you the name of a book to read - check that out.