I think that my problem with thinking of this as serious writing practice is because it's already a habit of mine and it feels like cheating to accept something that I already do and don't have to actively attempt to learn.
I write (and sometimes I get paid for it). To turn your diary writing into serious practice, I'd leave some blank pages after each entry, and after some time (a week perhaps) go back and try and rewrite an entry, or part of it, to be more clear, or have more impact.
When you are writing your diary, take some event or emotion from your day, and try to translate that into prose as if it were in a novel. It doesn't have to be long, or a scene, much of my writing in a novel is a piece less than a hundred words long, a paragraph or two, that describes an MC entering a new room, or meeting a new person, or ordering dinner.
Surely you did something during the day, or something made you laugh, or something irritated you momentarily. Perhaps you felt serene while grocery shopping. Pick a real moment you experienced during your day, and make a few paragraphs out of it. Read it a week later, and (on that blank page you left) try to rewrite it for more impact. Better word choices. More clarity. More sensory information -- Did you describe only what you saw? Did you hear anything? Smell anything? Was the air warm, or cold, or moving or still, stifling or dry?
Begin with actual moments from your life and memory; later you can move on to imaginary moments for characters.
Now these little descriptions are not stories, they don't have tension, or plot. As I answered in another recent question, these are vignettes, capturing a moment, like a photograph or painting does, but in words. But vignettes are a building block of scenes, and you can get practice adding tension and plots later. Vignettes that successfully create an imaginary experience for a reader are the bulk of writing well.
You can also write vignettes of dialogue you have actually had, conversations, being told a joke, relating some breaking news, etc. Practicing writing your real dialogue is practicing writing imagined dialogue. Get an idea of how much was actually communicated in words, how much detail, how long the sentences were. Actual dialogue is typically natural for someone, and by trying to recreate an actual conversation you had (without the hems, haws, and weird pauses), you get an idea of what dialogue should look like on the page. And, probably, how much thought actually goes with your dialogue.
Keeping a diary entry can be a good exercise, and writing about real life relieves you of the burden of imagining something. It is pre-imagined and you have all the detail you need, in your memory, to capture the moment. You have reality as your yardstick for how well you did (at least reality as you remember it.)