Thunderbird + K9 Mail are my way to go, too.
Though I mostly do like the redesign, since it fixes some long standing issues with Thunderbird (e.g. not being able to select a multi line message view ("cards view"), instead of the traditional table view.) The search bar being always on top annoys me each time I open it, so I understand a more long time Thunderbird user might have more nitpicks. Almost all of the changes can be reverted through settings, which I find awesome.
Using wev (wayland event viewer, which shows pressed keys) the side buttons show up as extra mouse buttons, so it should be possible to remap them.
PS: My old Logitech G710+ keyboard has some extra buttons which show up as normal numbers, which makes them pretty much useless. A while ago I found the now abandoned sidewinderd project which adds support for them. It's sad that those manufacturers don't create proper standards for these kind of things and instead hack it together somehow.