If you want after meal atmosphere go to dinner club. Restuarants depend on being able to turn tables to make a profit. If they are encouraging you to move along its because someone else is waiting for the table.
By sitting there you are costing the waiter and restuarant money.
Order some dessert if you want to hang out a while.
If the place is packed, I’ll move along. If there are obviously a lot of empty tables, I’ll feel fine in taking my time (but will remember that in my tip).
Now, if they are asking me to lift my feet so they can vacuum, that’s a clue I’ve been there too long...
If a restaurant is busy (IE - line waiting for table), then I rarely hang around. Not because of the waiter, but because I know how frustrated I get when I am waiting for a table and see folks just sitting and visiting for what seems like an endless time, thought there is a long wait for a table.
But if the establishment isn’t overflowing (as in, there are empty tables and not a big line), then I fail to see the harm in hanging around.
Dinner clubs are a rarity around here, but I wouldn’t visit them anyway - the dinner clubs I am familiar with exist for one primary reason - and it has nothing to do with eating - it has to do with loopholes in alcohol licensing in a dry county - and I won’t support that.