Is it time to extend his waking time and expect him to extend his naps?
No. It works the other way around.
When baby starts napping longer, they will therefore want to stay awake longer (because their last nap was longer) and so naps naturally space further apart and therefore a nap is "dropped".
So you need to wait until naps extend until naps start to be dropped. If you do it the other way, you'll just end up with an exhausted, over tired baby having fewer short naps.
You can either
(a) wait it out
(b) actively extend naps
If you just wait, babies naturally start to extend their daytime naps naturally. You don't have to do anything, just ensure baby gets enough sleep (so keep short naps very frequent) until it happens.
I actively worked-on extending naps. So I would keep naps in a place that allows for rhythmic movement, until they are extended. So no cot naps for mine until naps were longer than 90 minutes.
I favoured the bouncy chair. But pushchsir, swing, rocket, pram - these all work the same. The dummy is also invaluable for this.
So I'd bounce baby to sleep with the dummy. Then park nysekf on the sofa with bouncy chair at my feet, and periodically bounce for a bit, still for a bit. As soon as I see the first tiny sign of baby stirring, immediately start bouncing. Reinsert dummy if needed, keep that rhythmic, gentle bouncing going. The idea is to move baby from one sleep cycle into the next.
Initially it may not work, baby may just wake up. But sometimes baby will stay asleep instead of waking when stirring (and you do a silent cheer).
Again initially you may be needed to continually bounce through that second sleep cycle to keep it going. But in time, you can start easing off the bouncing and baby will stay asleep.
Then once this resetting is really established, baby should stop waking at all between sleep cycles. That's when you have longer naps.
I started doing this resetting at 3 months and my youngest had extended her naps to 90 minutes plus by 5 months - so it took 2 months of actively forcing naps to extend.
Once I was getting two longer naps per day, that's when I moved daytime naps in to the cot.