Unfortunately I realize making a change like this might cause a lot of code to break, and must be carefully considered.

Yes. And current behavior is came from MySQL-python.
There are no choice for now.

Thanks for the insight, I appreciate it.

See also: #396

I would think the (correct) behaviour can be achieved by setting a configuration parameter.
This can be either passed as argument to e.g. connect() or Connection(), or set at the package level itself (or even both: then the former should override the latter).

While backwards compatibility is something worth, in this case it is really unexpected, and the behaviour should at some point in the future be changed. Using a configuration parameter can ease that transition.

There is no correct behavior. DB-API 2.0 doesn't have __enter__ definition.
So you should prefer code without context manager, or you should use convenient wrapper.

I dislike configuration. There are too many options already. Many people asks
questions without reading docstring. When transition, I'll use normal deprecation process.

But problem is not backward compatibility.
Main problem is compatibility with well used but not maintained library: MySQL-python.

See also: PyMySQL/mysqlclient#44 and https://sourceforge.net/p/pypi/support-requests/553/

After it solved, I'll think about backward incompatible API changes with normal deprecation process.

I concur. The behaviour of the context manager was surprising to me but what it needs is better documentation, not another configuration knob. I solved that for me with a custom (and very simple) wrapper which explicitly implements whatever policy I wanted it to.

Proliferation of configuration knobs is IMO a bad thing: it explodes the number of cases to test and makes code harder to read.