The most well known open-source tool for all your email needs. Thanks to its ability for plugins it is also able to offer a comprehensive calendar (Lightning) and there are quite some addons to make notes. However syncing them to the cloud via CalDav is another topic. I generally recommend using tools specifically made for a certain task instead of cramming all of it into a single app.

The PIM Suite by the KDE team is an excellent choice if you want an all-in-one solution with KMail, Korganizer and KNotes as well as tools for to-do lists, RSS Feeds and even a journal. Of course you also can try each of these tools on itself.
Unfortunately, since it is part of the desktop environment KDE, it won’t neatly integrate with either GNOME (Pop!_OS, ZorinOS) or Cinnamon (Linux Mint).

The GNOME desktop environment (used as basis for Zorin OS as well as Pop!_OS) comes with well integrated tools that do their job very well. The Mail client is called Geary, with the others just being Calendar and Notes. Again, all of these can be downloaded and used on their own.
Their sync to clouds is managed through Online Accounts in your system settings.

An excellent to-do list app that integrates with your (GNOME) Desktop, got support for Cloud Synchronisation built-in as well as plugins to personalize the user experience further. Makes a great workflow addition together with the “Task Widget” Desktop Extension for GNOME on ZorinOS and Pop!_OS, adding your tasks next to your notifications and calendar on the desktop.

A very powerful Email client that integrates well with your desktop. If you’re used to Thunderbird but want to try something new, this one is definitely a good pick.

Even though being a Browser, Vivaldi does feature a built-in Email client, a calendar and can take notes. Together with the ability to sync to Vivaldi on your phone it can be quite compelling, however I’d still strongly suggest obtaining a Nextcloud anyway.
Sadly it’s on Google Chromium.

Unless you already got your Cloud tools running, you may want to look into Joplin. It is an extremely capable Notes-taking tool with collaboration abilities.

A powerful & visually pleasing Mail client with unique features aimed to streamline productivity and make yourself look as fabulous as you are to anyone you send emails to. Also offers a “Pro” version with more great features and does support connecting to an Office 365 account.

WebApps is a really handy tool to “natify” websites into desktop applications. Since many do like to use the web interface of email providers, they can put them into a desktop application using this. Only thing you need is an icon you want to use for the app (.png format) and a Browser that is also installed for WebApps to use (recommend Brave for this).
On Linux Mint it is a preinstalled app. The easiest way on the other distros is to download the newest .deb install package here.

These both are Email providers themselves that offer proper desktop apps as well as trustworthy Email accounts. If you’re also looking into a new Email provider, these might be a valid option.
Be aware that Tutanota does NOT support 3rd party email clients. Protonmail only does so with their “ProtonMail Bridge”, which might be hard to setup if you’re not used to do so.