I suspect the answer to this question is no, but I’ll ask anyway.
Is there a way to auto-sort tables within a base according to usage? So, for example, I click a button or enter a keyboard shortcut that sorts my tables from left to right based on activity within the tables. They would be sorted based on activity since the last time I ran the sort feature. So those tables with the most activity (new records and updates to records) would be sorted to the left while those with little or no activity would be sorted to the right. For those with the same level of activity that would sort alphabetically.
This is an interesting use case. However, currently this is not possible. Currently the only way to change the order of the tables is to manually drag them around (either by their tabs or in the menu listing all the tables).