My son is now 4, he also had quite a severe speech delay.
He started saying words clearly just before age 1 and then had covid very badly. It blocked his ears (we now know) and his speech stopped completely.
By age 2 he had virtually no speech, by age 3, he had a few words but none of them were clear.
I pushed and pushed but my HV team just kept telling me he was improving and would be eventually be ok. I had to push them, hard, for a referral to SALT and they kept messing it up so we lost a year between 2 and 3. After getting a clear hearing test after nearly a year of asking, I booked a private speech therapist who diagnosed him with a severe speech delay due to historical glue ear.
At the same time as we started with the speech therapist, I sent him to pre school, earlier than planned.
The 2 things combined made a world of difference. My son is like a different child. We worked really hard with the homework the speech therapist gave us and within 3 months, she signed him off. 3 months after that, his NHS SALT appointment came through and they also signed him straight off.
His speech is now crystal clear, his vocabulary is huge and advanced for his age (confirmed by pre school) and he is flying.
I know private speech therapy is not accessible to all but keep pushing at every avenue and start him in a childcare setting if you can. Speak slowly and reduce your words as starting point - simple 3 word sentences were our starting point. Instead of, 'right, let's go and get our shoes and put them on' we made it 'put shoes on' (just an example). It made an immediate impact.
We didn't even attempt potty training until his speech was up to it - pre school and our therapist agreed with this. We potty trained at 3 years, 3 months and he got it within 2 days and was dry overnight straightaway too. So please don't worry about that!
Best of luck to you, keep pushing.