There's an old saying that when you're looking for a spot for your brick-and-mortar business, the most important thing is "location, location, and location."
When learning piano improv, it's "consistency, consistency, and consistency."
This is as true with with rock and pop as it is with jazz and blues as well as classical and folk-based styles.
The challenge, as I've seen in my over 30 years of teaching experience, is that this approach is the complete opposite of how most pianists grew up learning the piano. The typical approach is to select a technically challenging piece and dive into it. You know that you'll either practice it for hours at a time or you simply won't learn it well enough.
The problem for most adult pianists who are getting into piano improv, is that this approach won't necessarily get you to where you want to go with your music. Especially with rock, pop, and folk music, I've seen some pianists spend hours upon hours learning challenging blues patterns, progressive rock ostinatos, and even some complex classic rock songs, only to find that they still can't sit down at their piano and easily play a song of their choice.
In other words, you're not yet fluent at playing rock or pop music.
To become fluent, consistency is the key, just as it is when learning a new language.
Becoming able to sit down at your piano, opening up a Beatles or Taylor Swift songbook, and playing something that sounds good within a few minutes is not a technically advanced skill. And it doesn't require that you wait 6 months until you have more "time" to get started.
You can start now.
5 minutes, 10 minutes, 15 minutes a day of playing songs will get you there, as long as you approach it in the right way. Don't get bogged down. Once you get a flow going and it becomes easy and joyful, you can begin learning the more advanced patterns and techniques. They'll feel more natural to you at that point in your musical development, just as we become fluent with language by learning the basic words well enough to hold conversations before we start memorizing lists of harder words.
Start by aiming for fluency. Consistency will get you there.
Enjoy the journey, and "let the music flow!"