This problem is rather obscure but I'll leave the solution here in case someone else runs into it and struggles to understand what's going on.
If you use Blender with a mouse that doesn't have a 3rd button, you can use either Alt or what Blender calls "OS-Key" to navigate: set it in Preferences ▶ Input ▶ Mouse ▶ Emulate 3 Button Mouse in Blender.
OS-Key is typically the Windows / Super key on a PC, or the ⌘ Command key on a Mac. In other words, for most of us, it's the magic i3 key.
Alt works fine. The problem comes if you want to use OS-Key instead in Blender and you have floating_modifier $mod defined in your ~/.config/i3/config file: Blender3 doesn't seem to mind sharing the key with i3, but Blender4 does.
If OS-Key doesn't work in Blender, try assigning floating_modifier to some other key, like Alt for example, like so:
floating_modifier $Mod1
Sadly there isn't. Not to my knowledge anyway: from what I've read, it's hard-coded. So unfortunately, the onus is on i3 to move over.