Web-based email client to manage email accounts independently

Web-based email client to manage email accounts independently

I'm looking for a web application that allows me to manage all my
different email accounts from a single place, but managing each email
account independently, I mean, having an inbox, sentbox, etc. for each
account... That's pretty much the same that I do with Thunderbird in my
desktop...
I know you can use Gmail, for example, to connect other email accounts
through IMAP or POP, but that way you have all the emails in a single list
and you have to use tags to organize them and so on...
What I'm looking for is something like you can see in the picture below,
but in a web-based application that I can access everywhere from any
device...

Note: I'm not asking for a recommendation among different applications,
but only about the existence of any application like this. Anyway, I'm not
sure if this questions fits here, if it doesn't, please excuse me...