My DS is 4.5 now and I would say he's 90% caught up, having had only about 4 words age 2. He did have speech therapy privately, started around 2.5 with only as he was only adding part words to his very small list. But I did loads with him to help, I wasn't doing the right things before.
You are with him so you are the best person to help. I learned from the therapy what to do. It's just simply repetition, lots of repetition, but you can theme your week- say farm week - animal names and noise, colours of animals, songs. Keep your "sentences" short, ideally just label 1-2 word best is Pig, pink pig, big pink, small pig, get the pig, pig there, oink,where's pig,? You still do other stuff, but the theme gets the repetition. Whilst it's great he understands you talking normally to copy language it needs to be more focused for some children and in context. Use toys and books with the theme in them.
If I point to a sheep for my baby child she says baa, that counts, that's a start of it. So nosies, songs all help.
Ideas are vehicle week,
colours,
space ( rockets, planets, stars, moon)
Zoo
Trains ( bridge, bag, track, women, man, boy, girl, choo)
Dolls,
Jobs - Doctors, nurses, vets, fire, police
Family ( with photos, video calls )
Then go back cover your weeks in a day, do zoo day and then farm day, repeat Trains week. You get the idea.