It doesn't sound like OP was talking about a business email account, does it? Even so, all the stuff you are saying is better in gmails web client (?) I can do in thunderbird.

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Yes but only locally on a single device.

Why, you never heard of IMAP?

I know imap but it only helps with synchronization… the tagging, sorting, automating, autoresponding all only works locally on your device. If your device is shut down, nothing will happen to incoming mails. Gmail does all these operations 24/7