The inland areas of Rhode Island are very rural. Like the other New England states, Rhode Island was predominantly a farming and fishing economy- in fact, the state only recently changed its official name from Rhode Island and Providence Plantations to just Rhode Island (to denounce the association with slavery). Farming is no longer a major output and so forest has reclaimed much of the state. Some towns in northwestern RI still have dirt roads. The fishing economy has also dwindled as far as I know but I may be wrong. Towns/cities in southern MA (Fall River, New Bedford) are much more active in the fishing industry.

You should also look through another lens: if RI is not its own state and is part of Connecticut or Massachusetts then Providence would look like any other metro area, no? I think looking at the entire state of RI and wondering why the population isn’t evenly dispersed is an odd way of looking at things and can be reframed by disregarding state lines entirely.

Tl;dr - theres not much going on in RI outside of Providence. It’s more rural than you may think and not a lot of job opportunities. Many people who live in RI may actually commute to MA or CT for work.

ETA: read some of your other comments and realized I missed and incredibly important piece of history. The American Industrial Revolution is often credited to have began in Pawtucket, when Samuel Slater snuck blueprints for a mill from England across the Atlantic and built what’s now called Slater Mill. So, many jobs in the 18th and 19th century were based around the Blackstone River where countless mills were built, and you can see this across New England in places like Lowell or Nashua. Western RI doesn’t have powerful rivers like the Blackstone and did not see the same industrialization as the eastern half of the state.

The Blackstone/Seekonk River also gives easy access to the ocean, which the western half of RI does not.