Cosine similarity between 0 and 1

You have a fair reason to prefer 0.0-1.0 (though many learning algorithms should do just fine with a -1.0 to 1.0 range). Your norm_sim rescaling of -1.0 to 1.0 to 0.0 to 1.0 is fine, if your only purpose is to get 0.0-1.0 ranges... but of course the resulting value isn't a true cosine-similarity anymore.

It won't necessarily matter that the values aren't real full-range angles any more. (If the algorithm needed real angles, it'd work with -1.0 to 1.0.)

Using the signless absolute value would be a bad idea, as it would change the rank order of similarities – moving some results that are "natively" most-dissimilar way up.

There's been work on constraining word-vectors to have only non-negative values in dimensions, & the usual benefit is that the resulting dimensions are more likely to be individually interpretable. (See for example https://cs.cmu.edu/~bmurphy/NNSE/.) However, gensim doesn't support this variant, & only trying it could reveal whether it would be better for any particular project.

Also, there's other research that suggests usual word-vectors may not be 'balanced' around the origin (so you'll see fewer negative cosine-similiarities than would be expected from points in a random hypersphere), and that shifting them to be more balanced will usually improve them for other tasks. See: https://arxiv.org/abs/1702.01417v2