Move from int to long int?

Summary:

I'm not sure where to post this as it's a Stan wide thing. Currently int values are just basic C int types with values from +/-2,147,483,647. Recently @bob-carpenter had a model with 1M parameters and it had me thinking that it's more realistic that we start having users try larger data sets in the future. For reference, a 10 column matrix of doubles with rows of length max int would be about 172 GB (8 * 2,147,483,647 * 10). Single machines are capable now of having 1TB of memory. While I think we are a few years away from having to worry about this it's something we should think about a little.

I think there's a few options for us

1. Have a stan::index alias that we use throughout all the repos. We can set this to long int, unsigned int, or whatever we want. (Eigen::Index is long int by default)
2. Add a long int to the language and have all the code that accepts integers be templated or use auto to deduce the int type. This is more work but lets users keep using int types without worry any loss in speed or memory size from larger integral types.

I'm personally fine with both. The only thing I feel strongly about is that we should keep using a signed type as the default for any index type

Current Version:

v2.34.1

The issue names no files, tests, or entry points. Start by surveying how integer and index types are used across the Stan repositories, then compare the proposed stan::index alias with adding a long int to the language. Done would require an agreed design and coordinated implementation scope, which the issue does not define.