For flexible project management look at Infinity:
It is not designed specifically for law practice. It is very flexible and can be configured all sorts of ways, and right now you can buy a lifetime deal: pay once and use it forever.
Also look at:
clickup
dubsado
monday
trello
Then of course there's law practice management software like:
Clio
Practice Panther
Both of which have lots of integrations and also work with Zapier.
MyCase is very popular as an all-in-one, but doesn't integrate with anything. More like a global solution if you just want one subscription that does most of everything for your law practice.
Perhaps check out Infinity. While not free, it's got a lifetime deal which is much cheaper than Asana.
You're better off paying for something than looking at free options. That way, you have support and updates, and you know they will stick around for a while.