I haven't seen one, and I suspect it wouldn't be a focus for startups. Job search tools targeted at job applicants are really difficult to make profitable, as opposed to hiring tools targeted at companies which have large budgets to spend.
That said, I suspect you're overcomplicating this. You shouldn't need to construct a database and elaborate systems for tracking every opportunity in detail. You may be spreading yourself too thin across so many different applications that you're unable to focus properly on the important ones, which is self-defeating.
For scheduling: Use your primary calendar tool, whatever it is. You don't want to add another calendar system to juggle.
For e-mails: Again, primary e-mail tool. If you're losing e-mails or forgetting to respond, you have bigger problems with your e-mail workflow. If you must, create a second inbox to manage nothing but applications and leave that window open all of the time so you can ignore whatever distractions are occurring in your primary inbox.
Discovery shouldn't be so complex that you need special tools to document it. Create a simple system like a Notion page for notes or a Google Doc for each company inside of a folder. You need this to be so simple that you can open it, write some notes down, and move on. The more complex you try to make it, the more you're going to struggle to get the basics done. Simple is key.
Finally: Learn to focus on the best opportunities. If you're getting too many opportunities to keep track of, start declining the least interesting or lowest-paying ones. Narrow your focus.