Package version number when upgrading to v0.6

Package version numbers are encouraged to use semver as described on the PkgDev GitHub page.

However, I am unsure how to apply this when upgrading a package to v0.6 where I drop support for older versions.
I suppose the change is backwards-incompatible, but going from 0.something to 1.0 when there are no API changes in the actual code seems like overkill to me.
I took a peek at the Distributions that apparently added a minor version to fit 0.6.

Are there any recommendations?

Minor version bump when below 1.0 is appropriate I think.

In particular:

Major version zero (0.y.z) is for initial development. Anything may change at any time. The public API should not be considered stable.

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As noted here, SemVer doesn’t specify semantics 0.x.y releases, but we consider the 0.x.y to be patch releases (bugfix only) while 0.x releases are major – anything can change. However, we do our best to deprecate changing functionality so that when you run your code you will get warnings telling you what you need to change. If you fix all the warnings after upgrading, with very few exceptions, your code should work as expected.

What would you suggest if I had a package with a major version of 1 or more? Would it still be a minor bump?