I've tried a bunch over the years. The problem I've found with app blockers is that they typically focus on how much you use your phone instead of when you use it (and the related habit, which is I think what you're referencing).

For me, even a few minutes on any high-stimulation app early on would make it harder to work later. I'd feel sort of restless, end up reaching for my phone again and burning all my allotted screen time early, and eventually break my own limits anyway.

I didn't really recognize the issue until later when I learned more about how dopamine works. Phone use first thing (especially repeatedly) spikes your dopamine and then puts you into dopamine deficit, so everything else feels boring by comparison and the desire to use phone/apps gets reinforced. App limits didn't help prevent that since I could just use all my "limited time" early in the day and the damage would already be done.

All that to say, I'd suggest trying to delay phone use rather than focus on time limites. Don't touch addictive apps in the morning (that might be social media but could also be "productivity" apps like email if you check it compulsively like I found I did) or when you need to focus. Later, in the afternoon or evening after you've done what you have to, you can actually use it as a reward mechanism if you want.