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Not just an app, but honestly I get all of this and more out of my nextcloud instance. There are mindmap plugins you can download as well as good task support that's well integrated with however many separate Calender's you want, etc. Its great!
The only downside is that on the mobile side of things you end up with a whole bunch of apps to sync and interface with the instance (nextcloud, etar, tasks.org, nextcloud notes etc)
maybe its our instance but calendar sync is horribly broken for us. I use thunderbird on pc and fossify calendar on mobile, and events tend to make it to nextcloud but not to the other devices pretty frequently.
Can't confirm, for me the contact, calendar and notes sync is running so smooth and maintenance-free, it feels close to magic.
On mobile I have etar calendar and davx5. It generally works pretty well, even if the sync is not instantaneous. I have a few problems with inviting people to events and sending the associated email/invitation, but it's just a matter of how the SMTP servers are managed, just a minor thing
This is pretty much my setup. I use nextcloud as a calendar, but for to-do lists I am experimenting with Joplin, with a mermaid plugin for also mindmaps. I'd like to automate everything and have a all-in-one solution but it does not look like an easy thing so far
It doesn't fit the bill perfectly but I've been using Obsidian with the Tasks and Day Planner plugins. Obsidian is no longer open source but I still like it because you have great control over your own data.
I use Syncthing to sync the notes between my phone and laptop (and select shared notes to the devices of my spouse).
The Day Planner plugins allows tasks to be time blocked / scheduled on a timeline of the day. There is also a week view and you can easily move from day to day.
You can sync your calendars so your calendar events automatically show on the timeline. Though I prefer to just check my calendar and enter the events manually.
The Tasks plugin lets you give tasks future or recurring due dates with some pretty flexible logic.
Aside from the day planning what I like the most is that I can also use this for journaling, to make project pages / dashboards, meeting minutes, and as a wiki. Take can live right with the appropriate information / context saving me from moving between multiple applications. I can save relevant attachments like emails in line with my notes and tasks just by dragging in the file (or directly dragging from an application like Outlook desktop).
In my opinion the sky is the limit with Obsidian. What I've described can feel a little rough around the edges but it works and the ability to build out your own process is unmatched. There are Kanban board plugins, drawing plugins (Excalidraw is amazing), and as for a mind map you can draw them or you can use built in view to see how all your notes link together.
I suggest watching some demo videos on Obsidian Day Planner plugin and Obsidian Tasks plugin, and Obsidian itself, and see what you think. You might be able to build out a system that works for you.