So I was playing around with this, and it looks like a good deal of the functionality that we want is actually already present, without automation rules. And it doesn’t even feel hacky, I think Coda’s designed to work like this on purpose.
What we can do
If you have a table with a lookup column (not formula), and then in that table being referenced, create a column with a formula that filters the rows referencing it (see embed below), then you add, remove, edit, delete, and create records from both tables from the perspective of either table.
Limitations
You just need, as others have mentioned, the details view. And it seems the formula must be =Filter(something) (ie, FormulaMap(), Lookup(), and probably other methods of generating rows work don’t work as well – either failing to display as tables in the view or unable to add rows). Therefore, it’s still not a truly bi-directional relationship, because one of them is still technically an uneditable formula.
I’ve written more notes about the possiblities and limitations of this kind of linking below.
UPDATE
Here’s an alternative method using multiple selects and buttons. I expected it to be pretty simple to set up, but my formulas ended up getting surprisingly convoluted… therefore it’s likely too much work / too complicated to be useful for most applications. But I’ll put it here anyway in case someone likes it. (same document, duplicated tables)