Add new variables for 1.16 and remove 1.13

This is the latest release. Updating is useful to ensure that we have
all of the latest fixes and enhancements.

Some operations are sensitive to the version of Go that is used. In
the past, formatting of source differed depending on the
version. Right now it is the content of the vendor directory which
changes when switch back and forth between 1.12 and 1.13.

We don't want to impose a certain workflow on developers, like forcing
all invocations of Go to run inside a container. If developers want
that, they can set up their development environment accordingly.

But we should warn about this aspect to raise awareness. "make"
invocations which involve Go now compare against the projects Go
version (specified in travis.yml) once at the beginning. This is only
a warning because we don't know which future version will be
compatible with the project.

Vendor directory handling gets updated, too: verification is now a
separate script (became too complex for make) and there is a
corresponding "update-vendor.sh". In contrast to verification,
updating vendor is not integrated into make and thus itself invokes
the go version check.

Go version 1.13, helper scripts

This avoids dependencies on the Go module cache or the upstream code
hosting.

prow.sh: use vendor directory if available