It's selling much better than PS3 6 months before replacement and with less price cuts, so I see they making a big cut when PS5 releases and supporting for another 3 years with one more final cut before finish.

A big price cut is coming before or at the PS5 launch. Big third party publishers and indie games will still support the PS4 to some extent until at least 2023. The hardware itself could be discontinued as early as 2022 or as late as 2024. I highly doubt we've got another PS2 situation where it takes almost 13 years to discontinue the hardware. We'll likely get Instant Library games until 2025 or 2026.
All in all, I don't fathom Sony dropping the PS4 like bad rubbish. Even the PS3 which underperformed (by PlayStation standards) still got some support and retail availability of the hardware for a while.

The last price cut PS3 had was in September 2012 when the cut the price to $269 and introduced a new model for $299, more than a year before PS4 launch, so there was a $269/299 PS3 against a $399 PS4, that’s why PS3 only sold around 8 million units more after PS4 launch.

This time is again on Sony‘s hands, the can cut it to $199(slim)/$299 (pro) or they can only do $250/350 or no price cut at all.

Sony has more incentive to keep the PS4 around than PS3. Sony is making billions from software and services. Physical sales, digital purchases, and PSN+ subscribers are thriving on the PS4. The revenue & profit the PS4 is bringing in has eclipsed every other Playstation console.

I don't think the PS4 will receive additional support from SIE (with exceptions like MLB The Show) but maybe we'll finally get the cut to $199.

PS5 trying to make a deal with PS4:

'You know the law we live by. Where is it written, beyond PS5 live lesser gamers, gamers too poor/late to enter the ecosystem, join next gen or turn a blind eye'?

'There's a peace that's only to be found on the other side of a generation war. If that battle must come, I will fight it!'

Years later:

It will depend on how quickly the user base is willing to transition. You can't just tell 100 million customers to do this or do that at the snap of a finger. There's the additional factor of the limited production of PS5s to consider as well. Also, no point in killing the old cow while it is still giving milk, just adjust the price as you go along.
The PS4 released 2013 but games for the PS3 were released up until 2018, so I'd say Sony has a pretty decent support policy.

Sony will reduce the Price for the PS4, but shift 90% Software support in 2021, to the PS5.
And from 2022 only PS5 support.

3rd Party is going to support the PS4 with cross gen Titels for next 3-4 years.

It won't look like the PS3.

Key developement infrastructure like Unreal Engine 4 & Unity will ensure PS4 is still receiving games years from now.
Many developers simply do not have the resources, expertise or even the ambition to dump the PS4. Diminishing returns is something we've seen benefit Switch (it's literally the only reason it exists tbh) where the average indie game isn't that demanding to warrant skipping the system, now imagine thats the average AA/AAA. I think PS4 will actually have a post succssor life similar and maybe even longer than the PS2 for this reason.

From an internal perspective sony may drop software support for it entirely this year, hwoever I still have a strong suspicion some titles announced are cross gen but they're choosing not to speak about the PS4 version and/or are actively discussing cancelling it.

But first party support doesn't mean that much when 99% of game sales on Playstation are third party anyway.

It'll be very interesting to see how a $199 PS4 performs in the coming years.

Also I think we will see maybe one more PS4 SKU in future.

The hardware can still be the driving force for PS Now, PSN subscriptions & an entry point to the playstation ecosystem.

So perhaps after not seeing a PS Three (a true slim version) we may get PSFour?