I suppose the best that can be done about that on-site is to have an alert that you can opt in to for whenever your pumpkin progresses stage, but that would still require you to visit the site itself, and well if you're already on the site then taking a look at the stage of your plants takes mere seconds.

As for having it 'ping' you while you're not on the site... uhh email? while it'd work, it certainly would be going above and beyond implementing a system that sends you an email every time your pumpkins progress stage. And that's not even taking into account other potential issues such as: your pumpkins not being planted all at the same time. The only way to accomodate that would be to have it alert you for every single pumpkin individually, which with some houses is a lot of alerts

So I think... while having more control over pumpkin stages would be nice (I keep missing sprouts lol, I totally get it), it's probably better to just utilize slow growth fertilizers to heighten chances. Or even better; making use of the fact that you know how much time pumpkin growth takes:

In the case of blooms, a pumpkin without fertilizer takes 11h to reach blooming stage (and stay that way for about 3 hours). So if you plant them at, say, 10am, you know that you'll be getting your blooms from 9pm to 12am. With that you can set reminders for yourself to make sure you remember to check when it's time. And with slow growth fertilizer, the whole process is slowed down, giving you more harvest time but also you will have to wait longer (about 16 hours for blooms I believe? But then you will also have ~5 hours to pick them up)

I didn't mean for this post to become so long but I hope it helps at least :0