This request has been effectively implemented on November 29th, 2022 as confirmed by V2Blast in this comment: (he was a CM at the time of posting the comment)
This was effectively implemented by the recent inbox improvements, so I'm marking this as [status-completed].
Among other changes and improvements to the inbox functionality, the following changes you requested were implemented:
The number in the top bar on the inbox button no longer disappears and everything is no longer marked as read.
The open/closed envelope icon toggles the read status of a message and the number in the top bar changes accordingly.
There is a [mark all as read] button which greys out when there are no more messages to read.
The following image demonstrates this: