I've been thinking about it myself - seems like a massive undertaking if you want to support all the different IMs that people use, but it might be possible to refurbish the chat-integration code from ferdi or the IM-bridges from Matrix in order to make it manageable.
You can also try Ferdi (hard fork of Franz with all features enabled always without payment) as an alternative to a paid Franz account.
(Full disclosure: I am a git comitter to Ferdi.)
It requires the phone because of the encryption. If you run it on Windows you won't be able to have the same chats if it works at all without a (different) phone number.
Also, check out Ferdi.
Have you tried something like ferdi? It's basically a chromium container around webapps. Not the best solution for for webapps you need to run anyway I've found it to work better than a standalone browser.
Maybe you could take a look at Ferdi? https://getferdi.com/
It's an open-source tool which connects to either their servers or a selfhosted one, and allows you to have multiple instances of the same social apps. (You can also use custom urls).
https://getferdi.com/ - Ferdi has been a lifesaver, helping me access WhatsApp, Slack, Skype, Telegram, Github, and a whole bunch of other resources from a single app. It even has a native Apple Silicon version.
Ferdi is an that makes having multiple accounts easier. Each service instance is it's own browsing space, so you can have any number of discord clients running through that (just uses the web discord interface).
So i was just getting my accounts into Ferdi, while i tried if ProtonMail has it's own app, then i noticed it's for paid accounts only.
Then i logged ProtonMail into Ferdi and it works normally.
I use MineTime for calendars and Thunderbird for tasks (a bit much if you aren't using it for email, too).
Ferdi is nice, too. It can integrate with Habitica, Todoist, etc.
I just keep HEY as one of my communication tools within Ferdi. Same features as the desktop app, but I can easily switch between email accounts, calendar, and Slack. Works great!
>For desktop I would prefer a wrapper for it to be a standalone program or something that this app will not be lost in one of my thousand browser tabs
maybe something like Ferdi?
There are client apps such as https://meetfranz.com/ and https://getferdi.com/ But I don't see Tutanota in Ferdi. Also maybe https://rambox.pro/#home ?
But these don't really "integrate" different services other than putting a common frame around them, maybe letting you manage notifications in one place, handling how they hibernate and re-log-in.
I know that you want to have a "real" alternative but 2 people has making a hard-fork of Franz named Ferdi. And Ferdi is Franz with all premium feature activated, no account needed, hibernation for the ram, dark mode...(and more) And they are trying to make it better. So if you want you can try ferdi at https://getferdi.com.
PS: you can export your Franz account if needed.